plumiEquation of a circle and tangents: Edexcel GCSE Maths questions
Every Edexcel 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 2H, Q22 (3 marks): The equation of circle A is x 2 + y 2 = 25 0 Circle A is translated by the vector to give circle B. 2 Sketch circle B. Show the coordinates of the centre o
- June 2025, Paper 3H, Q22 (4 marks): C is a circle with centre (0, 0) The straight line with equation 3x – 2y = 52 is the tangent to C at the point P. Find the coordinates of P. ( , )
- November 2024, Paper 1H, Q20 (4 marks): C is the circle with equation x 2 + y 2 = 4 Find an equation of the tangent to C at the point (p, 1) where p > 0 Give your answer in the form y ax b where a and
- June 2024, Paper 1H, Q23 (5 marks): C is a circle with centre (0, 0) L is a straight line. The circle C and the line L intersect at the points P and Q. The coordinates of P are (5, 10) The x coord
- November 2023, Paper 1H, Q21 (5 marks): (a) On the grid, draw the graph of x2 + y2 = 169 y 14 12 10 8 6 4 2 O x –14 –12 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 –2 –4 –6 –8 –10 –12 –14 (b) Use your graph to f
- June 2023, Paper 3H, Q23 (4 marks): A circle has equation x 2 + y 2 = 25 The point P with coordinates (–3, 4) lies on the circle. Alex says that the tangent to the circle at P crosses the x-axis a
- November 2022, Paper 2H, Q24 (4 marks): A circle has equation x2 + y2 = 12.25 The point P lies on the circle. The coordinates of P are (2.1, 2.8) The line L is the tangent to the circle at point P. Fi
- June 2022, Paper 1H, Q20 (4 marks): The centre of a circle is the point with coordinates (−1, 3) The point A with coordinates (6, 8) lies on the circle. Find an equation of the tangent to the circ
- November 2021, Paper 1H, Q20 (3 marks): The diagram shows the graph of x2 + y2 = 30.25 y 7 6 5 4 3 2 1 O x –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 –4 –5 –6 –7 Use the graph to find estimates for t
- November 2020, Paper 2H, Q22 (5 marks): C is a circle with centre the origin. A tangent to C passes through the points (–20, 0) and (0, 10) Work out an equation of C. You must show all your working.
- November 2018, Paper 2H, Q15 (1 mark): The equation of a circle is x2 + y2 = 42.25 Find the radius of the circle.
- June 2018, Paper 2H, Q16 (5 marks): (a) On the grid, draw the graph of x2 + y2 = 12.25 y 6 4 2 x O –6 –4 –2 2 4 6 –2 –4 –6 (b) Hence find estimates for the solutions of the simultaneous equations
- November 2017, Paper 3H, Q19 (5 marks): Prove algebraically that the straight line with equation xíy = 10 is a tangent to the circle with equation x2 + y2 = 20
- June 2017, Paper 1H, Q20 (5 marks): Solve algebraically the simultaneous equations x2 + y2 = 25 y – 3x = 13
- June 2017, Paper 2H, Q23 (3 marks): L is the circle with equation x2 + y2 = 4 ⎛ ⎞ P 3 7 ⎠⎟ is a point on L. , ⎝⎜ 2 2 Find an equation of the tangent to L at the point P.
- June 2017, Paper 3H, Q20 (4 marks): The equation of a curve is y = ax A is the point where the curve intersects the y-axis. (a) State the coordinates of A. ( , ) The equation of circle C is x2 + y
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