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{"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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": "<p>Write the equation of the hyperbola in standard form.</p>\n<p><em>(any decimal values should be rounded to 3 decimal places)</em></p>\n<p>[[0]] $=1$</p>", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}], "rulesets": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "name": "PreCal Find the equation of the hyperbola given foci and asymptotes", "statement": "<p>GIVEN:&nbsp; A hyperbola with foci $(0, \\pm \\var{c})$ and asymptotes $y=\\pm \\var{m}x$.</p>", "extensions": [], "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"}}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}]}], "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}