// Numbas version: finer_feedback_settings {"timing": {"timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}, "allowPause": true}, "duration": 0, "name": "PreCal CW Hyperbolas", "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "PreCal Find the parts of a Hyperbola", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["h", "k", "a", "b", "c", "orient", "choice", "vertex1", "vertex2", "transverse", "focus1", "focus2", "mAsymptoteNeg", "mAsymptotePos", "eccentricity", "orientTransverse"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "

Locate the center of the hyperbola. Enter your answer as: vector(x,y)

", "answer": "vector({h},{k})", "unitTests": [], "valuegenerators": [], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "patternmatch", "matchMode": "exact", "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "displayAnswer": "{orientTransverse[{choice}]}", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "answer": "{orientTransverse[{choice}]}", "unitTests": [], "customMarkingAlgorithm": "", "marks": 1}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

How is the transverse axis of the hyperbola oriented? (vertical or horizontal) [[0]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{vertex1[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{vertex2[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Locate the vertices of the hyperbola: Enter your answers as: vector(x,y)

Left/Bottom Vertex: [[0]]

Right/Top Vertex: [[1]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "numberentry", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "precision": "3", "showFeedbackIcon": true, "strictPrecision": false, "maxValue": "transverse[choice]", "correctAnswerFraction": false, "unitTests": [], "precisionMessage": "You have not given your answer to the correct precision.", "marks": 1, "precisionType": "dp", "mustBeReduced": false, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "precisionPartialCredit": "75", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "transverse[choice]", "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

What is the length of the transverse axis to three decimal places? [[0]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{focus1[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{focus2[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Locate the foci of the hyperbola. Enter your answer as vector(x,y) to 3 decimal places.

Left/Bottom Focus: [[0]]

Right/Top Focus: [[1]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{mAsymptoteNeg}*(x-{h})+{k}", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": "0.01", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{mAsymptotePos}*(x-{h})+{k}", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": "0.01", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equations of the asymptotes for this hyperbola.

Asymptote with Negative Slope: $y = $ [[0]]

Asymptote with Positive Slope: $y = $ [[1]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}], "rulesets": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "

GIVEN:

Hyperbola defined by: $\\Large{ \\simplify{ {orient}*(x-{h})^2/{a}^2-{orient}*(y-{k})^2/{b}^2=1 } }$

(Hint: Use Desmos graphing calculator to plot as you go and verify your answers.)

Locate the center of the hyperbola. Enter your answer as: vector(x,y)

How is the transverse axis of the hyperbola oriented? (vertical or horizontal) [[0]]

Locate the vertices of the hyperbola: Enter your answers as: vector(x,y)

Left/Bottom Vertex: [[0]]

Right/Top Vertex: [[1]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "numberentry", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "precision": "3", "showFeedbackIcon": true, "strictPrecision": false, "maxValue": "transverse[choice]", "correctAnswerFraction": false, "unitTests": [], "precisionMessage": "You have not given your answer to the correct precision.", "marks": 1, "precisionType": "dp", "mustBeReduced": false, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "precisionPartialCredit": "75", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "transverse[choice]", "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

What is the length of the transverse axis to three decimal places? [[0]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{focus1[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{focus2[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Locate the foci of the hyperbola. Enter your answer as vector(x,y) to 3 decimal places.

Left/Bottom Focus: [[0]]

Right/Top Focus: [[1]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{mAsymptoteNeg}*(x-{h})+{k}", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": "0.01", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{mAsymptotePos}*(x-{h})+{k}", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": "0.01", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equations of the asymptotes for this hyperbola.

Asymptote with Negative Slope: $y = $ [[0]]

Asymptote with Positive Slope: $y = $ [[1]]

GIVEN:

Hyperbola defined by: $\\Large{ \\simplify{ {orient}*(x-{h})^2/{a}^2-{orient}*(y-{k})^2/{b}^2=1 } }$

(Hint: Use Desmos graphing calculator to plot as you go and verify your answers.)

Locate the center of the hyperbola. Enter your answer as: vector(x,y)

How is the transverse axis of the hyperbola oriented? (vertical or horizontal) [[0]]

Locate the vertices of the hyperbola: Enter your answers as: vector(x,y)

Left/Bottom Vertex: [[0]]

Right/Top Vertex: [[1]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "numberentry", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "precision": "3", "showFeedbackIcon": true, "strictPrecision": false, "maxValue": "transverse[choice]", "correctAnswerFraction": false, "unitTests": [], "precisionMessage": "You have not given your answer to the correct precision.", "marks": 1, "precisionType": "dp", "mustBeReduced": false, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "precisionPartialCredit": "75", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "transverse[choice]", "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

What is the length of the transverse axis to three decimal places? [[0]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{focus1[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{focus2[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Locate the foci of the hyperbola. Enter your answer as vector(x,y) to 3 decimal places.

Left/Bottom Focus: [[0]]

Right/Top Focus: [[1]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{mAsymptoteNeg}*(x-{h})+{k}", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": "0.01", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{mAsymptotePos}*(x-{h})+{k}", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": "0.01", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equations of the asymptotes for this hyperbola.

Asymptote with Negative Slope: $y = $ [[0]]

Asymptote with Positive Slope: $y = $ [[1]]

GIVEN:

Hyperbola defined by: $\\Large{ \\simplify{ {orient}*(x-{h})^2/{a}^2-{orient}*(y-{k})^2/{b}^2=1 } }$

(Hint: Use Desmos graphing calculator to plot as you go and verify your answers.)

", "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"transverse": {"templateType": "anything", "definition": "[2*b,2*a]", "name": "transverse", "description": "", "group": "Ungrouped variables"}, "h": {"templateType": "anything", "definition": "random(-10..10)", "name": "h", "description": "", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "definition": "random(2..9 except a)", "name": "b", "description": "", "group": "Ungrouped variables"}, "k": {"templateType": "anything", "definition": "random(-10..10)", "name": "k", "description": "", "group": "Ungrouped variables"}, "choice": {"templateType": "anything", "definition": "(orient+1)/2", "name": "choice", "description": "", "group": "Ungrouped variables"}, "vertex1": {"templateType": "anything", "definition": "[vector(h,k-b),vector(h-a,k)]", "name": "vertex1", "description": "", "group": "Ungrouped variables"}, "orientTransverse": {"templateType": "anything", "definition": "[\"vertical\",\"horizontal\"]", "name": "orientTransverse", "description": "", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "random(2..10)", "name": "a", "description": "", "group": "Ungrouped variables"}, "mAsymptoteNeg": {"templateType": "anything", "definition": "-b/a", "name": "mAsymptoteNeg", "description": "", "group": "Ungrouped variables"}, "eccentricity": {"templateType": "anything", "definition": "c/a", "name": "eccentricity", "description": "", "group": "Ungrouped variables"}, "focus2": {"templateType": "anything", "definition": "[vector(h,k+c),vector(h+c,k)]", "name": "focus2", "description": "", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "definition": "sqrt(a^2+b^2)", "name": "c", "description": "", "group": "Ungrouped variables"}, "mAsymptotePos": {"templateType": "anything", "definition": "b/a", "name": "mAsymptotePos", "description": "", "group": "Ungrouped variables"}, "orient": {"templateType": "anything", "definition": "random([-1,1])", "name": "orient", "description": "", "group": "Ungrouped variables"}, "focus1": {"templateType": "anything", "definition": "[vector(h,k-c),vector(h-c,k)]", "name": "focus1", "description": "", "group": "Ungrouped variables"}, "vertex2": {"templateType": "anything", "definition": "[vector(h,k+b),vector(h+a,k)]", "name": "vertex2", "description": "", "group": "Ungrouped variables"}}, "type": "question"}, {"name": "PreCal Write the equation of the hyperbola from graph with Foci", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["h", "k", "a", "b", "c", "orient", "choice", "vertex1", "vertex2", "transverse", "focus1", "focus2", "mAsymptoteNeg", "mAsymptotePos", "eccentricity", "orientTransverse"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{orient}*(x-{h})^2/{a}^2-{orient}*(y-{k})^2/{b}^2", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "checkingType": "dp", "checkingAccuracy": "2", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the standard form equation of the parabola. You will need to round your value of $a^2$ or $b^2$ due to rounding of the foci locations. It should be an whole number.

[[0]] $=1$

GIVEN:

The hyperbola graphed below:

{geogebra_applet('https://www.geogebra.org/m/wvqauwgw',[ ['a',a], ['b',b], ['c',orient], ['F1',focus1[choice]], ['F2',focus2[choice]], ['h',h], ['k',k], ['A',vertex1[choice]], ['B',vertex2[choice]] ])}

", "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"transverse": {"templateType": "anything", "definition": "[2*b,2*a]", "name": "transverse", "description": "", "group": "Ungrouped variables"}, "eccentricity": {"templateType": "anything", "definition": "c/a", "name": "eccentricity", "description": "", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "definition": "random(2..9 except a)", "name": "b", "description": "", "group": "Ungrouped variables"}, "k": {"templateType": "anything", "definition": "random(-5..5)", "name": "k", "description": "", "group": "Ungrouped variables"}, "choice": {"templateType": "anything", "definition": "(orient+1)/2", "name": "choice", "description": "", "group": "Ungrouped variables"}, "vertex1": {"templateType": "anything", "definition": "[vector(h,k-b),vector(h-a,k)]", "name": "vertex1", "description": "", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "random(2..9)", "name": "a", "description": "", "group": "Ungrouped variables"}, "mAsymptoteNeg": {"templateType": "anything", "definition": "-b/a", "name": "mAsymptoteNeg", "description": "", "group": "Ungrouped variables"}, "h": {"templateType": "anything", "definition": "random(-5..5)", "name": "h", "description": "", "group": "Ungrouped variables"}, "focus2": {"templateType": "anything", "definition": "[vector(h,k+c),vector(h+c,k)]", "name": "focus2", "description": "", "group": "Ungrouped variables"}, "orientTransverse": {"templateType": "anything", "definition": "[\"vertical\",\"horizontal\"]", "name": "orientTransverse", "description": "", "group": "Ungrouped variables"}, "mAsymptotePos": {"templateType": "anything", "definition": "b/a", "name": "mAsymptotePos", "description": "", "group": "Ungrouped variables"}, "orient": {"templateType": "anything", "definition": "random([-1,1])", "name": "orient", "description": "", "group": "Ungrouped variables"}, "vertex2": {"templateType": "anything", "definition": "[vector(h,k+b),vector(h+a,k)]", "name": "vertex2", "description": "", "group": "Ungrouped variables"}, "focus1": {"templateType": "anything", "definition": "[vector(h,k-c),vector(h-c,k)]", "name": "focus1", "description": "", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "definition": "sqrt(a^2+b^2)", "name": "c", "description": "", "group": "Ungrouped variables"}}, "type": "question"}, {"name": "PreCal Write the equation of the hyperbola from graph with Foci", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["h", "k", "a", "b", "c", "orient", "choice", "vertex1", "vertex2", "transverse", "focus1", "focus2", "mAsymptoteNeg", "mAsymptotePos", "eccentricity", "orientTransverse"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{orient}*(x-{h})^2/{a}^2-{orient}*(y-{k})^2/{b}^2", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "checkingType": "dp", "checkingAccuracy": "2", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the standard form equation of the parabola. You will need to round your value of $a^2$ or $b^2$ due to rounding of the foci locations. It should be an whole number.

[[0]] $=1$

GIVEN:

The hyperbola graphed below:

", "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"transverse": {"templateType": "anything", "definition": "[2*b,2*a]", "name": "transverse", "description": "", "group": "Ungrouped variables"}, "eccentricity": {"templateType": "anything", "definition": "c/a", "name": "eccentricity", "description": "", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "definition": "random(2..9 except a)", "name": "b", "description": "", "group": "Ungrouped variables"}, "k": {"templateType": "anything", "definition": "random(-5..5)", "name": "k", "description": "", "group": "Ungrouped variables"}, "choice": {"templateType": "anything", "definition": "(orient+1)/2", "name": "choice", "description": "", "group": "Ungrouped variables"}, "vertex1": {"templateType": "anything", "definition": "[vector(h,k-b),vector(h-a,k)]", "name": "vertex1", "description": "", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "random(2..9)", "name": "a", "description": "", "group": "Ungrouped variables"}, "mAsymptoteNeg": {"templateType": "anything", "definition": "-b/a", "name": "mAsymptoteNeg", "description": "", "group": "Ungrouped variables"}, "h": {"templateType": "anything", "definition": "random(-5..5)", "name": "h", "description": "", "group": "Ungrouped variables"}, "focus2": {"templateType": "anything", "definition": "[vector(h,k+c),vector(h+c,k)]", "name": "focus2", "description": "", "group": "Ungrouped variables"}, "orientTransverse": {"templateType": "anything", "definition": "[\"vertical\",\"horizontal\"]", "name": "orientTransverse", "description": "", "group": "Ungrouped variables"}, "mAsymptotePos": {"templateType": "anything", "definition": "b/a", "name": "mAsymptotePos", "description": "", "group": "Ungrouped variables"}, "orient": {"templateType": "anything", "definition": "random([-1,1])", "name": "orient", "description": "", "group": "Ungrouped variables"}, "vertex2": {"templateType": "anything", "definition": "[vector(h,k+b),vector(h+a,k)]", "name": "vertex2", "description": "", "group": "Ungrouped variables"}, "focus1": {"templateType": "anything", "definition": "[vector(h,k-c),vector(h-c,k)]", "name": "focus1", "description": "", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "definition": "sqrt(a^2+b^2)", "name": "c", "description": "", "group": "Ungrouped variables"}}, "type": "question"}, {"name": "PreCal Find the equation of the hyperbola given foci and asymptotes", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["c", "m", "a", "b"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "y^2/{b}^2-x^2/{a}^2", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equation of the hyperbola in standard form.

(any decimal values should be rounded to 3 decimal places)

[[0]] $=1$

GIVEN: A hyperbola with foci $(0, \\pm \\var{c})$ and asymptotes $y=\\pm \\var{m}x$.

", "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"b": {"templateType": "anything", "definition": "m*a", "name": "b", "description": "", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "definition": "random(2..9)", "name": "c", "description": "", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "c/sqrt(1+m^2)", "name": "a", "description": "", "group": "Ungrouped variables"}, "m": {"templateType": "anything", "definition": "random(0.1..5#0.05)", "name": "m", "description": "", "group": "Ungrouped variables"}}, "type": "question"}, {"name": "PreCal Find the equation of the hyperbola given foci and asymptotes", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["c", "m", "a", "b"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "y^2/{b}^2-x^2/{a}^2", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equation of the hyperbola in standard form.

(any decimal values should be rounded to 3 decimal places)

[[0]] $=1$

GIVEN: A hyperbola with foci $(0, \\pm \\var{c})$ and asymptotes $y=\\pm \\var{m}x$.

GIVEN: A hyperbola with vertices at $(0,\\pm \\var{b})$ and asymptotes $y=\\pm \\var{m} x$

", "variables": {"m": {"definition": "random(0.25..5#0.25)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "m"}, "a": {"definition": "b/m", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a"}, "b": {"definition": "random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b"}}, "rulesets": {}, "functions": {}, "tags": [], "advice": "", "parts": [{"gaps": [{"vsetRange": [0, 1], "checkingType": "dp", "vsetRangePoints": 5, "customMarkingAlgorithm": "", "unitTests": [], "showCorrectAnswer": true, "checkingAccuracy": 3, "showPreview": true, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}, {"value": "", "name": "y"}], "marks": 1, "type": "jme", "showFeedbackIcon": true, "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}, "answer": "y^2/{b}^2-x^2/{a}^2", "failureRate": 1, "variableReplacements": [], "useCustomName": false, "checkVariableNames": false}], "sortAnswers": false, "type": "gapfill", "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "unitTests": [], "showCorrectAnswer": true, "prompt": "

Write the equation of the hyperboa in standard form:

(enter any decimal values to 3 decimal places)

[[0]] $=1$

GIVEN: A hyperbola with vertices at $(0,\\pm \\var{b})$ and asymptotes $y=\\pm \\var{m} x$

Write the equation of the hyperboa in standard form:

(enter any decimal values to 3 decimal places)

[[0]] $=1$

", "showFeedbackIcon": true, "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "marks": 0, "useCustomName": false}], "type": "question"}, {"name": "PreCal Find equation of the hyperbola given Vertices and Asymptotes", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["a", "m", "b"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "x^2/{a}^2-y^2/{b}^2", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equation of the hyperboa in standard form:

(enter any decimal values to 3 decimal places)

[[0]] $=1$

GIVEN: A hyperbola with vertices at $(\\pm \\var{a},0)$ and asymptotes $y=\\pm \\var{m} x$

", "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"b": {"templateType": "anything", "definition": "m*a", "name": "b", "description": "", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "random(1..9)", "name": "a", "description": "", "group": "Ungrouped variables"}, "m": {"templateType": "anything", "definition": "random(0.25..5#0.25)", "name": "m", "description": "", "group": "Ungrouped variables"}}, "type": "question"}, {"name": "PreCal Find equation of the hyperbola given Vertices and Asymptotes", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["a", "m", "b"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "x^2/{a}^2-y^2/{b}^2", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equation of the hyperboa in standard form:

(enter any decimal values to 3 decimal places)

[[0]] $=1$

GIVEN: A hyperbola with vertices at $(\\pm \\var{a},0)$ and asymptotes $y=\\pm \\var{m} x$

", "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"b": {"templateType": "anything", "definition": "m*a", "name": "b", "description": "", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "random(1..9)", "name": "a", "description": "", "group": "Ungrouped variables"}, "m": {"templateType": "anything", "definition": "random(0.25..5#0.25)", "name": "m", "description": "", "group": "Ungrouped variables"}}, "type": "question"}, {"name": "PreCal Find equation of the hyperbola given Vertices and Asymptotes", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["a", "m", "b"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "x^2/{a}^2-y^2/{b}^2", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equation of the hyperboa in standard form:

(enter any decimal values to 3 decimal places)

[[0]] $=1$

GIVEN: A hyperbola with vertices at $(\\pm \\var{a},0)$ and asymptotes $y=\\pm \\var{m} x$

GIVEN: A hyperbola with vertices at $(0,\\pm \\var{b})$ and asymptotes $y=\\pm \\var{m} x$

Write the equation of the hyperboa in standard form:

(enter any decimal values to 3 decimal places)

[[0]] $=1$

", "showFeedbackIcon": true, "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "marks": 0, "useCustomName": false}], "type": "question"}, {"name": "PreCal Find the equation of the hyperbola given foci and asymptotes", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["c", "m", "a", "b"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "y^2/{b}^2-x^2/{a}^2", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": 0.001, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equation of the hyperbola in standard form.

(any decimal values should be rounded to 3 decimal places)

[[0]] $=1$

GIVEN: A hyperbola with foci $(0, \\pm \\var{c})$ and asymptotes $y=\\pm \\var{m}x$.

", "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"b": {"templateType": "anything", "definition": "m*a", "name": "b", "description": "", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "definition": "random(2..9)", "name": "c", "description": "", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "c/sqrt(1+m^2)", "name": "a", "description": "", "group": "Ungrouped variables"}, "m": {"templateType": "anything", "definition": "random(0.1..5#0.05)", "name": "m", "description": "", "group": "Ungrouped variables"}}, "type": "question"}, {"name": "PreCal Find the parts of a Hyperbola", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["h", "k", "a", "b", "c", "orient", "choice", "vertex1", "vertex2", "transverse", "focus1", "focus2", "mAsymptoteNeg", "mAsymptotePos", "eccentricity", "orientTransverse"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "

Locate the center of the hyperbola. Enter your answer as: vector(x,y)

How is the transverse axis of the hyperbola oriented? (vertical or horizontal) [[0]]

Locate the vertices of the hyperbola: Enter your answers as: vector(x,y)

Left/Bottom Vertex: [[0]]

Right/Top Vertex: [[1]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "numberentry", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "precision": "3", "showFeedbackIcon": true, "strictPrecision": false, "maxValue": "transverse[choice]", "correctAnswerFraction": false, "unitTests": [], "precisionMessage": "You have not given your answer to the correct precision.", "marks": 1, "precisionType": "dp", "mustBeReduced": false, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "precisionPartialCredit": "75", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "transverse[choice]", "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

What is the length of the transverse axis to three decimal places? [[0]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{focus1[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{focus2[{choice}]}", "unitTests": [], "valuegenerators": [], "checkingType": "dp", "checkingAccuracy": 3, "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Locate the foci of the hyperbola. Enter your answer as vector(x,y) to 3 decimal places.

Left/Bottom Focus: [[0]]

Right/Top Focus: [[1]]

", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}, {"sortAnswers": false, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "gaps": [{"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{mAsymptoteNeg}*(x-{h})+{k}", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": "0.01", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}, {"checkVariableNames": false, "customName": "", "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{mAsymptotePos}*(x-{h})+{k}", "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}], "checkingType": "absdiff", "checkingAccuracy": "0.01", "marks": 1, "showPreview": true, "useCustomName": false, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "failureRate": 1, "vsetRangePoints": 5}], "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Write the equations of the asymptotes for this hyperbola.

Asymptote with Negative Slope: $y = $ [[0]]

Asymptote with Positive Slope: $y = $ [[1]]

GIVEN:

Hyperbola defined by: $\\Large{ \\simplify{ {orient}*(x-{h})^2/{a}^2-{orient}*(y-{k})^2/{b}^2=1 } }$

(Hint: Use Desmos graphing calculator to plot as you go and verify your answers.)

Write the standard form equation of the parabola. You will need to round your value of $a^2$ or $b^2$ due to rounding of the foci locations. It should be an whole number.

[[0]] $=1$

GIVEN:

The hyperbola graphed below:

", "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"transverse": {"templateType": "anything", "definition": "[2*b,2*a]", "name": "transverse", "description": "", "group": "Ungrouped variables"}, "eccentricity": {"templateType": "anything", "definition": "c/a", "name": "eccentricity", "description": "", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "definition": "random(2..9 except a)", "name": "b", "description": "", "group": "Ungrouped variables"}, "k": {"templateType": "anything", "definition": "random(-5..5)", "name": "k", "description": "", "group": "Ungrouped variables"}, "choice": {"templateType": "anything", "definition": "(orient+1)/2", "name": "choice", "description": "", "group": "Ungrouped variables"}, "vertex1": {"templateType": "anything", "definition": "[vector(h,k-b),vector(h-a,k)]", "name": "vertex1", "description": "", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "random(2..9)", "name": "a", "description": "", "group": "Ungrouped variables"}, "mAsymptoteNeg": {"templateType": "anything", "definition": "-b/a", "name": "mAsymptoteNeg", "description": "", "group": "Ungrouped variables"}, "h": {"templateType": "anything", "definition": "random(-5..5)", "name": "h", "description": "", "group": "Ungrouped variables"}, "focus2": {"templateType": "anything", "definition": "[vector(h,k+c),vector(h+c,k)]", "name": "focus2", "description": "", "group": "Ungrouped variables"}, "orientTransverse": {"templateType": "anything", "definition": "[\"vertical\",\"horizontal\"]", "name": "orientTransverse", "description": "", "group": "Ungrouped variables"}, "mAsymptotePos": {"templateType": "anything", "definition": "b/a", "name": "mAsymptotePos", "description": "", "group": "Ungrouped variables"}, "orient": {"templateType": "anything", "definition": "random([-1,1])", "name": "orient", "description": "", "group": "Ungrouped variables"}, "vertex2": {"templateType": "anything", "definition": "[vector(h,k+b),vector(h+a,k)]", "name": "vertex2", "description": "", "group": "Ungrouped variables"}, "focus1": {"templateType": "anything", "definition": "[vector(h,k-c),vector(h-c,k)]", "name": "focus1", "description": "", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "definition": "sqrt(a^2+b^2)", "name": "c", "description": "", "group": "Ungrouped variables"}}, "type": "question"}, {"name": "PreCal Classifying Conics from their non-standard equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "functions": {}, "ungrouped_variables": ["A", "C", "D", "F", "G", "opt2", "opt3", "opt4", "choice", "classify"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "patternmatch", "variableReplacements": [], "adaptiveMarkingPenalty": 0, "matchMode": "exact", "displayAnswer": "{classify[{choice}]}", "marks": 1, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "answer": "{classify[{choice}]}", "unitTests": [], "showCorrectAnswer": true, "customMarkingAlgorithm": ""}], "rulesets": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "variables": {"opt4": {"templateType": "anything", "definition": "award(3,A*C<0)", "name": "opt4", "description": "", "group": "Ungrouped variables"}, "classify": {"templateType": "anything", "definition": "[\"Circle\",\"Parabola\",\"Ellipse\",\"Hyperbola\"]", "name": "classify", "description": "", "group": "Ungrouped variables"}, "G": {"templateType": "anything", "definition": "random(-5..5)", "name": "G", "description": "", "group": "Ungrouped variables"}, "opt2": {"templateType": "anything", "definition": "award(1,A*C=0)", "name": "opt2", "description": "", "group": "Ungrouped variables"}, "C": {"templateType": "anything", "definition": "random(-5..5 except 0)", "name": "C", "description": "", "group": "Ungrouped variables"}, "opt3": {"templateType": "anything", "definition": "award(2,A*C>0 and A<>C)", "name": "opt3", "description": "", "group": "Ungrouped variables"}, "choice": {"templateType": "anything", "definition": "opt2+opt3+opt4", "name": "choice", "description": "", "group": "Ungrouped variables"}, "F": {"templateType": "anything", "definition": "random(-20..20)", "name": "F", "description": "", "group": "Ungrouped variables"}, "A": {"templateType": "anything", "definition": "random(-6..6)", "name": "A", "description": "", "group": "Ungrouped variables"}, "D": {"templateType": "anything", "definition": "random(-20..20)", "name": "D", "description": "", "group": "Ungrouped variables"}}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "advice": "", "statement": "

GIVEN: $\\simplify{ {A}x^2 + {C}y^2 + {D}x + {F}y +{G} = 0 }$