// Numbas version: exam_results_page_options
{"name": "complex loci (circles 5)", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "complex loci (circles 5)", "tags": [], "metadata": {"description": "<p>given random circle on graph with centre in 2nd or 3rd quadrant. find loci in complex form</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>The Argand diagram below shows a locus of points lying on a circle.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/srgctpyu',defs)}</p>", "advice": "<p>The circle on the Argand diagram has a centre of $(\\var{a}, \\var{b})$ and radius $\\var{c}$. This means that all the points on the circle are a distance of $\\var{c}$ from $(\\var{a}, \\var{b})$</p>\n<p>We can write this in the form $|z-z_1|=a$ which states that the distance between $z$ and $z_1$ is equal to $a$</p>\n<p>For this questin then $|z-z_1|=a$ becomes&nbsp;</p>\n<p>\\[|z-(\\simplify{{a}+{b}i})|=\\var{c}\\]</p>\n<p>which can also be written as</p>\n<p>\\[|\\simplify{z-{a}-{b}i}|=\\var{c}\\]</p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-6 .. -1#1)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-6,-5,-4,-3,-2,-1,1,2,3,4,5,6)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2 .. 6#1)", "description": "", "templateType": "randrange", "can_override": false}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['a',a],\n  ['b',b],\n  ['c',c],\n  ]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "defs"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "<p>Write an equation that defines the locus of points shown.</p>\n<ul>\n<li>if needed you can pan and zoom the graph</li>\n<li>give your answer in terms of $z$</li>\n<li>to write the modulus brackets you should input abs()\n<ul>\n<li>For example writing abs(x-1) will create the expression $|x-1|$</li>\n</ul>\n</li>\n</ul>\n<p></p>\n<p></p>\n<p></p>", "answer": "abs(z-({a}+{b}i))={c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": "10", "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "z", "value": "random(c+a+b*i,random(0..1#0))"}]}], "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/"}]}