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1.3.4 Coordinate geometry of a circle - Questions\",\"description\":\"Practise 1.3.4 Coordinate geometry of a circle A Level Maths exam-style questions with worked solutions on MathsGenie.\",\"learningResourceType\":\"Practice questions\",\"educationalLevel\":\"A Level\",\"about\":{\"@type\":\"Thing\",\"name\":\"1.3.4 Coordinate geometry of a circle\"},\"url\":\"https://mathsgenie.co.uk/a-level/maths/ocr/coordinate-geometry-of-a-circle/questions/q3\",\"inLanguage\":\"en-GB\",\"provider\":{\"@id\":\"https://mathsgenie.co.uk/#organization\"}}"}}],["$","div",null,{"className":"min-h-0 w-full flex-1 overflow-hidden bg-background","children":["$","$L3b",null,{"backHref":"/a-level/maths/ocr/questions","basePath":"/a-level/maths/ocr/coordinate-geometry-of-a-circle/questions","formulaUrl":null,"initialIndex":2,"initialQuestionWindow":[{"id":"185832ef-034d-4aed-8445-1d8a6ac0de62","revisionId":"27e44c8d-9864-4ae4-bd71-194f822ac5b1","questionNumber":null,"questionType":"MC","specification":"One of the equations below is the equation of a circle of radius $6$.\n\nIdentify this equation.\n\nTick one box.","difficulty":null,"difficultyBand":"easy","tier":null,"totalMarks":1,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[],"options":[{"id":"60949d8c-53ea-4e64-b9d8-aaee5fe4dd89","content":"$$(x - 4)^2 + (y + 1)^2 = 6$","correct":false,"markscheme":null,"order":0,"metadata":null},{"id":"c04a3d57-569a-42bb-b7c1-d72f88be4b6d","content":"$$(x - 4)^2 + (y + 1)^2 = 36$","correct":true,"markscheme":"- B1\n\nThe centre-radius form is $(x-a)^2 + (y-b)^2 = r^2$, so the right-hand side must be $6^2 = 36$. (A) gives radius $\\sqrt6$; (C) is not a circle; (D) has no real points.","order":1,"metadata":null},{"id":"467e0f41-e18a-48a2-b6c3-dc0bed5e1fe5","content":"$$(x - 4)^2 - (y + 1)^2 = 36$","correct":false,"markscheme":null,"order":2,"metadata":null},{"id":"49bf7529-acd3-48a3-b528-51831ba2cd67","content":"$$(x - 4)^2 + (y + 1)^2 = -36$","correct":false,"markscheme":null,"order":3,"metadata":null}],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"3480aee1-1709-4356-b885-e1b52f4efe81","revisionId":"f08c31dc-dc9c-4633-ab0f-8a094b8575cd","questionNumber":null,"questionType":"LA","specification":"The circle $C$ has centre $(-3, 4)$ and is tangent to the $y$-axis.","difficulty":null,"difficultyBand":"easy","tier":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"isCalculation":false,"parts":[{"id":"c6077107-69c1-4bba-aada-213a4a7b3aa0","label":null,"content":"Find an equation for $C$.","markscheme":"- The radius is the perpendicular distance from $(-3,4)$ to the $y$-axis, so $r=3$ B1\n- Uses the centre-radius form $(x+3)^2+(y-4)^2=r^2$ M1\n- $(x+3)^2+(y-4)^2=9$ A1\n\nThe distance to the $y$-axis is $|-3|=3$; a radius of $4$ comes from using the distance to the $x$-axis.","marks":3,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"44c6cb13-283c-44fc-8a1e-98b2bda28cb7","revisionId":"a5c19920-c89c-4bbd-8af3-dd2e0651e481","questionNumber":null,"questionType":"LA","specification":"The circle $C$ has equation\n$x^2+y^2+4x-6y+4=0$.","difficulty":null,"difficultyBand":"easy","tier":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"isCalculation":false,"parts":[{"id":"34970647-c351-4dfd-9be7-df0a5cc9b5f5","label":null,"content":"Determine whether the origin lies inside, on or outside $C$.","markscheme":"- Completes the square to obtain $(x+2)^2+(y-3)^2=9$ M1\n- The centre is $(-2,3)$ and the radius is $3$ A1\n- The distance from the origin to the centre is $\\sqrt{13}>3$, so the origin lies outside $C$ B1\n\nAccept substitution of $(0,0)$ into $(x+2)^2+(y-3)^2=9$: the left-hand side is $13>9$, so the point is outside.","marks":3,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"a_level_maths__ocr","summaries":[{"id":"10913190-807f-4295-9a0f-0b487305eebd","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"185832ef-034d-4aed-8445-1d8a6ac0de62","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"MC","isCalculation":true},{"id":"3480aee1-1709-4356-b885-e1b52f4efe81","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"36da95e6-f942-4d53-b453-a67c483f9974","difficultyBand":"hard","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"44c6cb13-283c-44fc-8a1e-98b2bda28cb7","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"7ce28a30-fa91-49f3-919d-c4e2d340851d","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"8f17724b-1eff-4d8b-b0ae-945f53a5454f","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"9473ae54-ac54-4077-875c-554b029c06fb","difficultyBand":"hard","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false}],"title":"1.3.4 Coordinate geometry of a circle","topicId":"b8ce414f-7f6f-4bb5-ace0-b013b17beec0","topicSidebar":"$L3c","topicSlug":"coordinate-geometry-of-a-circle","topicTitle":"1.3.4 Coordinate geometry of a circle"}]}],"$L3d","$L3e"]}]

1.3.4 Coordinate geometry of a circle

Question 2

1.3.4 Coordinate geometry of a circle Questions

1.3.4 Coordinate geometry of a circle

Question 2

1.3.4 Coordinate geometry of a circle Questions