// Numbas version: exam_results_page_options
{"name": "Centre and radius of a circle", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-5..5)", "description": "", "name": "b"}, "r": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..6)", "description": "", "name": "r"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-5..5)", "description": "", "name": "a"}}, "ungrouped_variables": ["a", "r", "b"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "name": "Centre and radius of a circle", "showQuestionGroupNames": false, "functions": {}, "parts": [{"scripts": {}, "gaps": [{"answer": "{a}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"showStrings": false, "message": "<p>Input all numbers as fractions or integers as appropriate and not as decimals.</p>", "strings": ["."], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "std", "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}, {"answer": "{b}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"showStrings": false, "message": "<p>Input all numbers as fractions or integers as appropriate and not as decimals.</p>", "strings": ["."], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "std", "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}, {"answer": "{r}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"showStrings": false, "message": "<p>Input all numbers as fractions or integers as appropriate and not as decimals.</p>", "strings": ["."], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "std", "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>The centre is ([[0]],[[1]]). The radius is [[2]].</p>", "showCorrectAnswer": true, "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "\n    <p>Find the centre and radius of the circle with equation</p>\n    <p>\\[\\simplify[std]{x^2+y^2 -{2*a}x -{2*b}y+{a^2+b^2-r^2}}=0.\\] </p>  \n     <p>Input the coordinates of the centre and the radius as integers.</p>\n  \n  \n    ", "tags": ["SFY0001", "centre", "checked2015", "equation of a circle", "radius", "standard form"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n        \t\t\n        \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Find the centre and radius of a circle when given an equation in standard form.</p>"}, "advice": "\n    <p>Complete the square for each of $x$ and $y$: $~~~\\simplify[std]{x^2-{2*a}x =(x-{a})^2-{a^2}}$ and $\\simplify[std]{y^2 -{2*b}y=(y-{b})^2-{b^2}}$.</p>\n  <p>Therefore $\\simplify[std]{x^2+y^2 -{2*a}x -{2*b}y+{a^2+b^2-r^2}=(x-{a})^2-{a^2}+(y-{b})^2-{b^2}+{a^2+b^2-r^2}}$</p>\n  <p>and the equation of the circle becomes $\\simplify[std]{(x-{a})^2+(y-{b})^2={r^2}}$.</p>\n  <p>It follows that the centre is $(\\var{a}, \\var{b})$ and the radius is $\\var{r}$. </p>\n    ", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}