// Numbas version: exam_results_page_options
{"name": "complex loci (circles)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "complex loci (circles)", "tags": [], "metadata": {"description": "<p>given equation of locus in form |z-a|=bfind centre and radius. multiple choice question</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "", "advice": "<p>$|z-z_1|=a$ means that the distance between $z$ and $z_1$ is equal to $a$</p>\n<p>$|z-(\\simplify{{a}+{b}i})|=\\var{c}$ thus means that the distance between $z$ and $\\simplify{{a}+{b}i}$ is equal to $\\var{c}$</p>\n<p>The points that are a distance of $\\var{c}$ from $\\simplify{{a}+{b}i}$ can be drawn as a circle with radius $\\var{c}$ and centre $(\\var{a}, \\var{b})$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5,-4,-3,-2,-1,1,2,3,4,5)", "description": "<p>x coordinate of centre</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-5,-4,-3,-2,-1,1,2,3,4,5)", "description": "<p>y coordinate of centre</p>", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2 .. 8#1)", "description": "<p>radius</p>", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "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>Describe the locus of points given by $|z-(\\simplify{{a}+{b}i})|=\\var{c}$</p>\n<p></p>\n<p></p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["A circle with centre $(\\var{a}, \\var{b})$ and radius $\\var{c}$", "A circle with centre $(\\var{a}, \\var{b})$ and radius $\\simplify{{c}^2}$", "A circle with centre $(\\simplify{0-{a}}, \\simplify{0-{b}})$ and radius $\\var{c}$", "A circle with centre $(\\simplify{0-{a}}, \\simplify{0-{b}})$ and radius $\\simplify{{c}^2}$"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mike Phipps", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14139/"}]}]}], "contributors": [{"name": "Mike Phipps", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14139/"}]}