plumiCoordinate geometry in the (x, y) plane: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P2.3 Coordinate geometry in the (x, y) plane, 2019–2025, with its mark scheme and examiner’s report.
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All 20 questions on Coordinate geometry in the (x, y) plane, as a list
- June 2025, AS Pure 2 (P2), Q2 (7 marks): The line joining the points (–2, 5) and (4, 15) is the diameter of a circle C. (a) Find an equation for C. (b) Hence find the exact coordinates of the point on
- June 2025 (A), AS Pure 2 (P2), Q9 (5 marks): The circle C • has a centre which lies on the x‑axis • touches the y‑axis • passes through the point (5, 6) (a) On Diagram 1, sketch a graph of C. (b) Find an e
- January 2025, AS Pure 2 (P2), Q6 (8 marks): O P M l y x A(–1, 2) B(11, 6) Figure 2 The point A (–1, 2) and the point B (11, 6) both lie on a circle with centre P. The point M is the midpoint of AB. Given
- October 2024, AS Pure 2 (P2), Q10 (10 marks): The circle C has equation x 2 + y 2 + 4x – 30y + 209 = 0 (a) Find (i) the coordinates of the centre of C, (ii) the exact value of the radius of C. The line L ha
- June 2024, AS Pure 2 (P2), Q7 (6 marks): The circle C1 has equation x 2 + y 2 + 8x – 10y = 29 (a) (i) Find the coordinates of the centre of C1 (ii) Find the exact value of the radius of C1 In part (b)
- June 2024 (R), AS Pure 2 (P2), Q3 (5 marks): A circle has equation x 2 + y 2 + 8x – 14y – 79 = 0 (a) Find (i) the coordinates of the centre of the circle, (ii) the radius of the circle. Given that P is the
- January 2024, AS Pure 2 (P2), Q3 (6 marks): The circle C • has centre A(3, 5) • passes through the point B(8, – 7) (a) Find an equation for C. The points M and N lie on C such that MN is a chord of C. Giv
- October 2023, AS Pure 2 (P2), Q7 (8 marks): X (4, –3) O N l C x y Figure 2 Figure 2 shows a sketch of • the circle C with centre X (4, –3) • the line l with equation y x 5 2 55 2 Given that l is the tange
- June 2023, AS Pure 2 (P2), Q3 (7 marks): A circle C has centre (2, 5) Given that the point P(8, –3) lies on C (a) (i) find the radius of C (ii) find an equation for C (b) Find the equation of the tange
- January 2023, AS Pure 2 (P2), Q6 (10 marks): The circle C has equation x2 + y2 + 8x – 4y = 0 (a) Find (i) the coordinates of the centre of C, (ii) the exact radius of C. The point P lies on C. Given that t
- October 2022, AS Pure 2 (P2), Q9 (12 marks): In this question you must show detailed reasoning. Solutions relying entirely on calculator technology are not acceptable. R O A T C1 C2 x y l Figure 3 Figure 3
- June 2022, AS Pure 2 (P2), Q3 (7 marks): (i) Show that the following statement is false: “ (n + 1)3 − n3 is prime for all n ∈ ” (ii) Given that the points A(1, 0) , B(3, −10) and C(7, −6) lie on a ci
- June 2022, AS Pure 2 (P2), Q10 (12 marks): The circle C has centre X (3, 5) and radius r The line l has equation y = 2x + k , where k is a constant. (a) Show that l and C intersect when 5x2 + (4k − 26)x
- January 2022, AS Pure 2 (P2), Q6 (8 marks): y x O P(23, 14) R(–7, –26) Q(15, –30) Figure 1 The points P(23, 14), Q(15, –30) and R(–7, –26) lie on the circle C, as shown in Figure 1. (a) Show that angle PQ
- October 2021, AS Pure 2 (P2), Q6 (8 marks): (i) The circle C1 has equation x2 + y2 + 10x − 12y = k where k is a constant (a) Find the coordinates of the centre of C1 (b) State the possible range in values
- June 2021, AS Pure 2 (P2), Q6 (7 marks): A circle has equation x2 – 6x + y2 + 8y + k = 0 where k is a positive constant. Given that the x-axis is a tangent to this circle, (a) find the value of k. The
- January 2021, AS Pure 2 (P2), Q9 (10 marks): A circle C has equation (x − k) 2 + ( y − 2k) 2 = k + 7 where k is a positive constant. (a) Write down, in terms of k, (i) the coordinates of the centre of C, (
- October 2020, AS Pure 2 (P2), Q4 (9 marks): The points P and Q have coordinates (–11, 6) and (–3, 12) respectively. Given that PQ is a diameter of the circle C, (a) (i) find the coordinates of the centre
- January 2020, AS Pure 2 (P2), Q6 (8 marks): The circle C has equation x2 + y2 + 6x – 4y – 14 = 0 (a) Find (i) the coordinates of the centre of C, (ii) the exact radius of C. The line with equation y = k,
- June 2019, AS Pure 2 (P2), Q2 (7 marks): A circle C has equation x2 + y2 + 4x – 10y – 21 = 0 Find (a) (i) the coordinates of the centre of C, (ii) the exact value of the radius of C. The point P(5, 4)
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