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{"name": "Luis's copy of Intersection of a straight line and a circle", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Luis's copy of Intersection of a straight line and a circle", "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s1", "m", "l", "n", "q", "p", "b1", "k", "t"], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"js": "", "css": ""}, "tags": ["SFY0001", "checked2015", "equation of a circle", "equation of a straight line", "quadratic equation"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "type": "question", "variables": {"d": {"name": "d", "templateType": "anything", "description": "", "definition": "random(-5..5)", "group": "Ungrouped variables"}, "s1": {"name": "s1", "templateType": "anything", "description": "", "definition": "random(-1,1)", "group": "Ungrouped variables"}, "b": {"name": "b", "templateType": "anything", "description": "", "definition": "b1+d", "group": "Ungrouped variables"}, "m": {"name": "m", "templateType": "anything", "description": "", "definition": "if(a<c,a,c)", "group": "Ungrouped variables"}, "f": {"name": "f", "templateType": "anything", "description": "", "definition": "(b-d)/(a-c)", "group": "Ungrouped variables"}, "b1": {"name": "b1", "templateType": "anything", "description": "", "definition": "random(-2,2,-4,4)", "group": "Ungrouped variables"}, "p": {"name": "p", "templateType": "anything", "description": "", "definition": "if(a<c,c,a)", "group": "Ungrouped variables"}, "q": {"name": "q", "templateType": "anything", "description": "", "definition": "if(a<c,d,b)", "group": "Ungrouped variables"}, "k": {"name": "k", "templateType": "anything", "description": "", "definition": "(a+c+t*d-t*b)/2", "group": "Ungrouped variables"}, "c": {"name": "c", "templateType": "anything", "description": "", "definition": "a+Random(2,4)*s1", "group": "Ungrouped variables"}, "a": {"name": "a", "templateType": "anything", "description": "", "definition": "random(1,-1)*random(1..4)", "group": "Ungrouped variables"}, "l": {"name": "l", "templateType": "anything", "description": "", "definition": "(b+d+t*a-t*c)/2", "group": "Ungrouped variables"}, "g": {"name": "g", "templateType": "anything", "description": "", "definition": "(b*c-a*d)/(c-a)", "group": "Ungrouped variables"}, "t": {"name": "t", "templateType": "anything", "description": "", "definition": "random(-5..5 except 0)", "group": "Ungrouped variables"}, "n": {"name": "n", "templateType": "anything", "description": "", "definition": "if(a<c,b,d)", "group": "Ungrouped variables"}}, "variable_groups": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": []}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Find the points of intersection of a straight line and a circle.</p>", "notes": "\n    \t\t\n    \t\t"}, "parts": [{"prompt": "<p>([[0]],[[1]]) and ([[2]],[[3]])</p>", "gaps": [{"checkvariablenames": false, "vsetrange": [0, 1], "vsetrangepoints": 5, "answersimplification": "std", "type": "jme", "expectedvariablenames": [], "scripts": {}, "marks": 1, "checkingaccuracy": 0.001, "checkingtype": "absdiff", "answer": "{m}", "showCorrectAnswer": true, "showpreview": true, "notallowed": {"message": "<p>Input all numbers as fractions or integers as appropriate and not as decimals.</p>", "strings": ["."], "showStrings": false, "partialCredit": 0}}, {"checkvariablenames": false, "vsetrange": [0, 1], "vsetrangepoints": 5, "answersimplification": "std", "type": "jme", "expectedvariablenames": [], "scripts": {}, "marks": 1, "checkingaccuracy": 0.001, "checkingtype": "absdiff", "answer": "{n}", "showCorrectAnswer": true, "showpreview": true, "notallowed": {"message": "<p>Input all numbers as fractions or integers as appropriate and not as decimals.</p>", "strings": ["."], "showStrings": false, "partialCredit": 0}}, {"checkvariablenames": false, "vsetrange": [0, 1], "vsetrangepoints": 5, "answersimplification": "std", "type": "jme", "expectedvariablenames": [], "scripts": {}, "marks": 1, "checkingaccuracy": 0.001, "checkingtype": "absdiff", "answer": "{p}", "showCorrectAnswer": true, "showpreview": true, "notallowed": {"message": "<p>Input all numbers as fractions or integers as appropriate and not as decimals.</p>", "strings": ["."], "showStrings": false, "partialCredit": 0}}, {"checkvariablenames": false, "vsetrange": [0, 1], "vsetrangepoints": 5, "answersimplification": "std", "type": "jme", "expectedvariablenames": [], "scripts": {}, "marks": 1, "checkingaccuracy": 0.001, "checkingtype": "absdiff", "answer": "{q}", "showCorrectAnswer": true, "showpreview": true, "notallowed": {"message": "<p>Input all numbers as fractions or integers as appropriate and not as decimals.</p>", "strings": ["."], "showStrings": false, "partialCredit": 0}}], "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "marks": 0}], "advice": "\n  <p>Substitute for $y = \\simplify[std]{({b-d}/{a-c})x+{b*c-a*d}/{c-a}}$ in the equation of the circle.</p>\n    <p>We get $\\simplify[std]{x^2+(({b-d}/{a-c})x+{b*c-a*d}/{c-a})^2 -{2*k}x -{2*l}(({b-d}/{a-c})x+{b*c-a*d}/{c-a})+{2*k*a+2*l*b-a^2-b^2}}=0$.</p>\n    <p>Collecting terms we get $\\simplify[std]{{1+ (b-d)^2/(a-c)^2} x^2+{(-2)*(b-d)(b*c-a*d)/(a-c)^2-2*k  -(2*l)*(b-d)/(a-c)}x+{(b*c-a*d)^2/(c-a)^2 -2*l*(b*c-a*d)/(c-a)+2*k*a+2*l*b-a^2-b^2}}=0$.</p>\n    <p>Solving this quadratic equation for $x$ gives solutions $x=\\var{a}$ and $x=\\var{c}$.</p>\n    <p>Substitute these values of $x$ into the equation $\\simplify[std]{({b-d}/{a-c})x+{b*c-a*d}/{c-a}}$ to obtain the $y$-coordinates: $y=\\var{b}$ (when $x=\\var{a}$) and $y=\\var{d}$ (when $x=\\var{c}$).</p>\n    <p>Enter the coordinate pairs in the order $(\\var{m},\\var{n})$, $(\\var{p}, \\var{q})$. </p>\n  ", "statement": "\n  <p>Find the points where:</p>\n    <ul>\n    <li>the straight line $y = \\simplify[std]{({b-d}/{a-c})x+{b*c-a*d}/{c-a}}$</li>\n    </ul>\n    <p>&nbsp;</p>\n    <ul>\n    <li>and the circle $\\simplify[std]{x^2+y^2 -{2*k}x -{2*l}y+{2*k*a+2*l*b-a^2-b^2}}=0$</li>\n    </ul>\n    <p>&nbsp;</p>\n    meet.\n    <p>&nbsp;</p>\n    \n    <p>Enter the coordinates for the two points, starting with the point with the smaller $x$-coordinate.</p>\n    <p>Note that, for example, $-3$ is smaller than $-1$. Thus if the points of intersection were $(-1, 4)$ and $(-3,6)$ you would enter $(-3,6)$ for the first point and $(-1, 4)$ for the second.</p>\n    <p>Input the coordinates as integers.</p>\n    \n    \n  ", "functions": {}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}