plumiEllipse and hyperbola: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 4.2 Ellipse and hyperbola, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 8 questions on Ellipse and hyperbola, as a list
- June 2025, Further Pure 1, Q8 (7 marks): The ellipse E has equation x y 2 2 64 36 1 The line l has equation y = mx + c where m and c are constants. (a) Show that the x coordinates of the points of inte
- June 2024, Further Pure 1, Q6 (6 marks): The ellipse E has equation x y 2 2 25 9 1 The hyperbola H has equation x a y b 2 2 2 2 1 where a and b are positive constants. Given that • the eccentricity of
- June 2023, Further Pure 1, Q4 (12 marks): The ellipse E has equation x y 2 2 16 9 1 (a) Determine the exact value of the eccentricity of E (2) The points P(4 cos θ, 3 sin θ) and Q(4 cos θ, –3 sin θ) lie
- June 2022, Further Pure 1, Q1 (7 marks): An ellipse has equation x y 2 2 16 4 1 and eccentricity e 1 A hyperbola has equation x a y b 2 2 2 2 1 and eccentricity e 2 Given that e 1 × e 2 = 1 (a) show th
- November 2021, Further Pure 1, Q1 (5 marks): The ellipse E has equation x y 2 2 36 20 1 + = Find (a) the coordinates of the foci of E, (3) (b) the equations of the directrices of E. (2)
- November 2021, Further Pure 1, Q5 (9 marks): The parabola C has equation y 2 = 32x and the hyperbola H has equation x y 2 2 36 9 1 − = (a) Write down the equations of the asymptotes of H. (1) The line l1 i
- November 2020, Further Pure 1, Q5 (7 marks): The ellipse E has equation x y 2 2 36 16 1 + = The points S and S ′ are the foci of E. (a) Find the coordinates of S and S ′ (3) (b) Show that for any point P o
- June 2019, Further Pure 1, Q8 (14 marks): The hyperbola H has equation x y 2 2 16 9 1 − = The line l1 is the tangent to H at the point P(4cosh ș, 3sinh ș). The line l1 meets the x-axis at the point A. T
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