plumiEquation of a circle and tangents: OCR GCSE Maths questions
Every OCR GCSE Maths exam question on A16 Equation of a circle and tangents, 2017–2025, with its mark scheme and examiner’s report.
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All 16 questions on Equation of a circle and tangents, as a list
- June 2025, Paper 4, Q17 (5 marks): The diagram shows a circle, centre (0, 0). y 4 x -4 4 O -4 (a) Write down the equation of the circle. (a) (b) Point A has coordinates (2.3, 3.3). Show that poin
- June 2025, Paper 6, Q21 (5 marks): The graph of y x intersects the graph of x y 70 at two points. + = Work out the exact coordinates of the two points. You must show your working. ( , ) and ( , )
- June 2024, Paper 6, Q19 (5 marks): The diagram shows a circle with centre (0, 0) and a tangent at (12, 5 - ) crosses the x-axis at (p, 0). The tangent at (12, 5 y Not to scale x O p (12, ) 5 - Fi
- November 2023, Paper 4, Q20 (6 marks): The diagram shows a circle, centre the origin, with the tangent to the circle at the point (4, 2). y 20 (4, 2) x O - 20 20 - 20 (a) Write down the equation of t
- June 2023, Paper 6, Q18 (9 marks): (a) Describe fully the graph of x 20 . y + = 2 2 (b) The graph of y 3 10 intersects the graph of x 20 at two points. x y = + + = Use an algebraic method to work
- November 2022, Paper 6, Q18 (9 marks): A circle has equation x 100 . y + = The sketch shows the circle and two points, A and B, which lie on the circumference of the circle. y A x O B (a) Write down
- June 2022, Paper 4, Q18 (2 marks): The diagram shows a circle, centre the origin. y 3 -3 3 O x -3 Write down the equation of the circle.
- June 2022, Paper 5, Q19 (7 marks): The graph below shows a circle with centre (0, 0) and equation x2 + y2 = 169. y 13 x -13 O 13 -13 (a) Show that the point (-12, 5) lies on the circumference of
- November 2021, Paper 5, Q19 (4 marks): The point 5 7 , 2 Find the equation of the circle.
- November 2020, Paper 4, Q18 (4 marks): Here is a sketch of the circle 45 . x y + = y 45 x O - 45 45 - 45 1 . (a) Show that the tangent to this circle at the point (-3, 6) has a gradient of 2 (b) Find
- November 2019, Paper 4, Q14 (5 marks): The diagram shows a circle with centre (0, 0) and a tangent at the point (–12, 16). y Not to scale (–12, 16) x O The tangent crosses the y-axis at the point (0,
- November 2019, Paper 5, Q21 (6 marks): In this question all units are in cm. 2 2 A circle has equation x y 36 . + = (a) Write down the radius and centre of the circle. (a) radius: cm centre: ( , ) (b
- June 2019, Paper 6, Q19 (6 marks): The point -( 5 2 lies on the circumference of a circle, centre (0, 0). , ) (a) Find the equation of the circle. (a) (b) Work out the gradient of the tangent to
- November 2018, Paper 6, Q17 (5 marks): Find the exact coordinates of the two intersections of the line y 2 and the circle x 2 2 30 . x y = + = y y = 2x x2 + y2 = 30 Not to scale x O ( , ) and ( , )
- November 2017, Paper 6, Q17 (8 marks): The diagram shows a circle, centre the origin. y 10 5 x 0 –10 –5 5 10 –5 –10 (a) Write down the equation of the circle. (a) (b) Point P has coordinates (8, –6).
- June 2017, Paper 4, Q17 (2 marks): Describe fully the graph which has the equation x y 9 . + =
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