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Uses the point $A(-4, 3)$: $y - 3 = -\\dfrac{5}{2}(x + 4)$ M1\n- $5x + 2y + 14 = 0$ A1\n\nAccept any integer multiple. Award A0 for $y = -\\frac52 x - 7$, since the required form is specified.","marks":4,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"22b656c1-ab6f-4abe-bdbe-d8e9c811da25","revisionId":"538e4d89-77db-496f-ac32-2f4047c4427c","questionNumber":null,"questionType":"LA","specification":"The circle $C$ has centre $(-1, 4)$ and passes through the point $(3, 7)$.","difficulty":null,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"isCalculation":false,"parts":[{"id":"b1c6b527-8619-4330-9d8a-5efc1db65218","label":null,"content":"Find an equation for $C$.","markscheme":"- Uses $(x + 1)^2 + (y - 4)^2 = r^2$ M1\n- $r^2 = (3 + 1)^2 + (7 - 4)^2 = 16 + 9 = 25$ A1\n- $(x + 1)^2 + (y - 4)^2 = 25$ A1\n\nAccept the expanded form $x^2 + y^2 + 2x - 8y - 8 = 0$. Award A1A0 for stopping at $r = 5$ without writing the equation.","marks":3,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"24ec727e-e88a-494e-90d6-48286b3f903b","revisionId":"1a1e8040-0fd7-4676-a3a9-75ecfcc2ebca","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","totalMarks":1,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[],"options":[{"id":"3dc52f81-6fe3-44ea-86b1-a8e2905988b6","content":"$$(x - 4)^2 + (y + 1)^2 = 6$","correct":false,"markscheme":null,"order":0,"metadata":null},{"id":"25d78029-77ab-4af9-9973-579854bee007","content":"$$(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":"e6058968-34cb-4e71-aabf-7cad73ba3fbe","content":"$$(x - 4)^2 - (y + 1)^2 = 36$","correct":false,"markscheme":null,"order":2,"metadata":null},{"id":"d7acc160-03a7-4d0b-9188-5396fe266ca4","content":"$$(x - 4)^2 + (y + 1)^2 = -36$","correct":false,"markscheme":null,"order":3,"metadata":null}],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"a_level_maths__aqa","summaries":[{"id":"04397ad9-539f-4b9c-8543-44d330f26060","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"a3813ac5-bdc3-44db-875c-814eef87f47f","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"76d0d06f-ae1b-4e27-a2d1-b92a0cdb207c","difficultyBand":"medium","calculatorUse":null,"totalMarks":10,"questionType":"LA","isCalculation":true},{"id":"38bbcc6f-ee92-4b6c-9c58-9cba1368d288","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"57a05292-724a-4415-b86f-bf2ba107ce2c","difficultyBand":"medium","calculatorUse":null,"totalMarks":10,"questionType":"LA","isCalculation":true},{"id":"16f68ee3-8f29-4a97-a422-8b00679792ed","difficultyBand":"medium","calculatorUse":null,"totalMarks":10,"questionType":"LA","isCalculation":true},{"id":"7b46030e-fce1-4c03-bf95-b5bd7c44b91a","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"a706a638-6483-49ee-bc7f-7025352d1f36","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"2c2c1bf7-3cd4-48ac-b817-a7e32cbd3184","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":false},{"id":"1848eb90-1f58-4bbc-ad3c-ad9bea1bd2c4","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"c2a89d37-c9e9-47f9-8e7b-82f4b7c6de9d","difficultyBand":"hard","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"17a12418-a336-4fd5-9e95-491ebd3449bc","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"acc64ca4-9dd5-4b73-a407-79bbdb44d8f2","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"bb212c95-89b6-4a6a-a907-4665dfe1faea","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"f4f4a7ac-f35f-440a-8c48-fb0bb407af42","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"c95e57ba-4fca-4b18-8349-c97052702260","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"6f44eb9d-12e7-42b8-a813-ce6448801be3","difficultyBand":"hard","calculatorUse":null,"totalMarks":12,"questionType":"LA","isCalculation":true},{"id":"adcfd298-9ebc-499f-bcb4-2e49bf761893","difficultyBand":"hard","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"abbf1d7b-ff54-4df2-8aad-b0cf338d24a9","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"34324838-9381-43ca-b3f2-dde5af9bc537","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"c9477b41-b6d4-40e7-8040-6cf6be4c217d","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"792afe89-92b4-44ae-86ef-bec9826419cf","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"c7b0a9fe-3b11-4876-bb2e-e8f4b9d0d7ee","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"70917b6c-1c89-4fad-8602-c8a5c042c528","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"d8677ba9-5b6c-454a-8c59-ff463b29d3fe","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"bdb981cd-5a19-4f3c-8764-ace97b6ffd74","difficultyBand":"hard","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"11f96c43-79dc-4322-855d-1ebaaf350154","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"00da04d1-de98-42a8-a532-eff85225b98f","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"01697cac-0fe6-4c7f-af2a-ee8e403cbfd7","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"02343ae6-4ab9-4e67-baba-074a9516e65d","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"023f5d89-da63-43ce-9120-0306439c8c9b","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"06aa0830-f6dc-4aa5-a566-d5c7235c7561","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"0cb5768f-aa3a-4ea7-a71d-65a42908a943","di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Coordinate geometry of the circle","topicId":"97fb69d0-5e0c-4206-b14f-5c6b3dbc19e1","topicSidebar":"$L3b","topicSlug":"coordinate-geometry-of-the-circle","topicTitle":"1.6.2 Coordinate geometry of the circle"}]}],"$L3c","$L3d"]}]

1.6.2 Coordinate geometry of the circle

Question 7

1.6.2 Coordinate geometry of the circle Questions

1.6.2 Coordinate geometry of the circle

Question 7

1.6.2 Coordinate geometry of the circle Questions