// Numbas version: finer_feedback_settings
{"name": "2.6.1 Task 5", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/HELM2_fig26.png", "/srv/numbas/media/question-resources/HELM2_fig26.png"], ["question-resources/HELM2_fig27.png", "/srv/numbas/media/question-resources/HELM2_fig27.png"], ["question-resources/HELM2_6_Task3.PNG", "/srv/numbas/media/question-resources/HELM2_6_Task3.PNG"], ["question-resources/HELM2_6_Task3a.png", "/srv/numbas/media/question-resources/HELM2_6_Task3a.png"], ["question-resources/HELM2_6_Task4.png", "/srv/numbas/media/question-resources/HELM2_6_Task4.png"], ["question-resources/HELM2_fig29.png", "/srv/numbas/media/question-resources/HELM2_fig29.png"], ["question-resources/HELM2_6_Task6.png", "/srv/numbas/media/question-resources/HELM2_6_Task6.png"], ["question-resources/HELM2_fig30.png", "/srv/numbas/media/question-resources/HELM2_fig30.png"], ["question-resources/HELM2_fig28.png", "/srv/numbas/media/question-resources/HELM2_fig28.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "2.6.1 Task 5", "tags": [], "metadata": {"description": "<p>Write down the equation of a circle centre C and radius R.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write down the equation of the following circle for which the centre $C$ and radius $R$ are given:</p>", "advice": "<p>$x_0 = \\var{Cx}$, $y_0 = \\var{Cy}$ and $R^2=\\var{Rv^2}$ so by Equation (2) the circle's equation is $\\var{simplify(expression(\"(x-\"+Cx+\")^2+(y-\"+Cy+\")^2\"),\"all\")}=\\var{R2}$</p>\n<p>{graph}</p>", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Cx": {"name": "Cx", "group": "The circle", "definition": "random(-5..5)", "description": "", "templateType": "anything", "can_override": false}, "Cy": {"name": "Cy", "group": "The circle", "definition": "random(-5..5)", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "The circle", "definition": "if (Rv=1 or Rv=4,0,random(0,1))", "description": "", "templateType": "anything", "can_override": false}, "Rv": {"name": "Rv", "group": "The circle", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "The circle", "definition": "if(idx=0,Rv,sqrt(Rv))", "description": "", "templateType": "anything", "can_override": false}, "rd": {"name": "rd", "group": "The circle", "definition": "if(idx=0,R,latex(\"\\\\sqrt{\"+Rv+\"}\"))", "description": "<p>Radius for display purposes</p>", "templateType": "anything", "can_override": false}, "R2": {"name": "R2", "group": "The circle", "definition": "if(idx=0,Rv^2,Rv)", "description": "", "templateType": "anything", "can_override": false}, "graph": {"name": "graph", "group": "The graph", "definition": "jessiecode(\n  400,400,[{xmin},{ymax},{xmax},{ymin}],\"r={R};Cx={Cx};Cy={Cy};\"+safe(\n  \"\"\"\n    X = point(-Cx,-r-Cy) <<visible: false>>;\n    Y = point(r-Cx,0-Cy) <<visible: false>>;\n    Z = point(-r-Cx,0-Cy) <<visible: false>>;\n    circle(X,Y,Z) << strokeOpacity: 0.3 >>;\n    C=point(-Cx,-Cy) <<color:'blue', name:''>>;\n    segment(C,Y);\n  \"\"\"),\n  [\n    \"axis\": true\n  ]\n)", "description": "", "templateType": "anything", "can_override": false}, "xmin": {"name": "xmin", "group": "The graph", "definition": "min(-1,-Cx-ceil(R)-1)", "description": "", "templateType": "anything", "can_override": false}, "xmaxtemp": {"name": "xmaxtemp", "group": "The graph", "definition": "max(1,-Cx+ceil(R)+1)", "description": "", "templateType": "anything", "can_override": false}, "ymin": {"name": "ymin", "group": "The graph", "definition": "min(-1,-Cy-ceil(R)-1)", "description": "", "templateType": "anything", "can_override": false}, "ymaxtemp": {"name": "ymaxtemp", "group": "The graph", "definition": "max(1,-Cy+ceil(R)+1)", "description": "", "templateType": "anything", "can_override": false}, "xmax": {"name": "xmax", "group": "The graph", "definition": "if(xmaxtemp-xmin > ymaxtemp-ymin,xmaxtemp,xmin+ymaxtemp-ymin)", "description": "", "templateType": "anything", "can_override": false}, "ymax": {"name": "ymax", "group": "The graph", "definition": "if(ymaxtemp-ymin > xmaxtemp-xmin,ymaxtemp,ymin+xmaxtemp-xmin)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "The circle", "variables": ["Cx", "Cy", "idx", "Rv", "R", "rd", "R2"]}, {"name": "The graph", "variables": ["graph", "xmin", "xmaxtemp", "ymin", "ymaxtemp", "xmax", "ymax"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"padding-left: 40px;\">$C\\,(\\var{Cx},\\var{Cy}),\\;R=\\var{Rd}\\;$</p>\n<p style=\"padding-left: 40px;\">Equation: [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "(x-{Cx})^2+(y-{Cy})^2={R^2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.1", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": "sqrt(4-(y-2)^2)"}, {"name": "y", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}