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circle $C$ has equation\n$x^2+y^2-2x+6y=26$.","difficulty":null,"difficultyBand":"medium","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"d7b1e42f-07c5-4a0a-a4d9-6e04fc9acac7","label":null,"content":"Find the coordinates of the points where $C$ intersects the $y$-axis.","markscheme":"- Sets $x=0$ to obtain $y^2+6y-26=0$ M1\n- Completes the square: $(y+3)^2=35$ M1\n- $y=-3\\pm\\sqrt{35}$ A1\n- The intersection points are $(0,-3+\\sqrt{35})$ and $(0,-3-\\sqrt{35})$ A1\n\nAccept use of the quadratic formula. Both points are required in coordinate form.","marks":4,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"7ce28a30-fa91-49f3-919d-c4e2d340851d","revisionId":"cb282c33-d789-4004-9611-8a376ed15176","questionNumber":null,"questionType":"LA","specification":"The centre of a circle lies on the $x$-axis. The points $A(1,4)$ and $B(5,2)$ lie on the circle.","difficulty":null,"difficultyBand":"medium","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":false,"parts":[{"id":"4e21932c-d47a-4a68-ad45-31aade257c13","label":null,"content":"Find an equation of the circle.","markscheme":"- Lets the centre be $(a,0)$ and equates squared distances: $(1-a)^2+4^2=(5-a)^2+2^2$ M1\n- Solves $17-2a=29-10a$ to obtain $a=\\dfrac32$ A1\n- $r^2=\\left(1-\\dfrac32\\right)^2+16=\\dfrac{65}{4}$ M1\n- $\\left(x-\\dfrac32\\right)^2+y^2=\\dfrac{65}{4}$ A1\n\nEquating the two squared radii avoids introducing square roots. Accept the equivalent equation $4x^2+4y^2-12x-56=0$.","marks":4,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"8f17724b-1eff-4d8b-b0ae-945f53a5454f","revisionId":"7da6f30d-ec7d-44f0-b24d-8189b49cbfba","questionNumber":null,"questionType":"LA","specification":"The circle $C$ has equation\n$x^2 + y^2 + 8x - 4y + k = 0$\nwhere $k$ is a constant.\n\n$C$ passes through the point $(1, 5)$.","difficulty":null,"difficultyBand":"medium","tier":null,"totalMarks":5,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"72c69343-3326-48c5-a118-43c1fab13ac2","label":"a","content":"Find the value of $k$.","markscheme":"- Substitutes $(1, 5)$: $1 + 25 + 8 - 20 + k = 0$ M1\n- $14 + k = 0$, so $k = -14$ A1","marks":2,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]},{"id":"613b49f6-ac54-46a2-af8c-0a7cc0f94f24","label":"b","content":"Rewrite the equation of $C$ in centre-radius form, then state its centre and exact radius.","markscheme":"- Completes the square: $(x + 4)^2 + (y - 2)^2 = 16 + 4 + 14 = 34$ M1\n- Centre $(-4, 2)$ A1\n- Radius $= \\sqrt{34}$ A1\n\nFollow through from their value of $k$. Exact form required for the radius.","marks":3,"order":1,"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