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Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$
"}, "showQuestionGroupNames": false, "statement": "You are given the equation $\\simplify{(x-{a})^2+(y-{b})^2={rs}}$.
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", "showCorrectAnswer": true, "type": "gapfill"}, {"marks": 0, "gaps": [{"correctAnswerFraction": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "minValue": "{a}", "maxValue": "{a}", "scripts": {}, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "allowFractions": false, "variableReplacements": []}, {"correctAnswerFraction": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "minValue": "{b+r}", "maxValue": "{b+r}", "scripts": {}, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "allowFractions": false, "variableReplacements": []}, {"correctAnswerFraction": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "minValue": "{a}", "maxValue": "{a}", "scripts": {}, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "allowFractions": false, "variableReplacements": []}, {"correctAnswerFraction": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "minValue": "{b-r}", "maxValue": "{b-r}", "scripts": {}, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "allowFractions": false, "variableReplacements": []}, {"correctAnswerFraction": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "minValue": "{a-r}", "maxValue": "{a-r}", "scripts": {}, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "allowFractions": false, "variableReplacements": []}, {"correctAnswerFraction": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "minValue": "{b}", "maxValue": "{b}", "scripts": {}, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "allowFractions": false, "variableReplacements": []}, {"correctAnswerFraction": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "minValue": "{a+r}", "maxValue": "{a+r}", "scripts": {}, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "allowFractions": false, "variableReplacements": []}, {"correctAnswerFraction": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "minValue": "{b}", "maxValue": "{b}", "scripts": {}, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "allowFractions": false, "variableReplacements": []}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": [], "prompt": "The above information allows us to find four points of the circle easily:
\nThe equation of a circle with radius $r$ and centre $(a,b)$ is $(x-a)^2+(y-b)^2=r^2$.
\n