plumiParabola and rectangular hyperbola: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 4.1 Parabola and rectangular 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 12 questions on Parabola and rectangular hyperbola, as a list
- June 2025, AS Further Pure 1, Q5 (9 marks): The parabola C has equation y 2 = 16x The point P (4t 2 , 8t) lies on C. (a) Show that an equation for the tangent to C at P is yt – x = 4t 2 (3) The line l pas
- June 2024, Further Pure 1, Q8 (8 marks): The parabola P has equation y 2 = 4ax, where a is a positive constant. The point A at at 2 2 , , where t ≠ 0, lies on P. (a) Use calculus to show that an equati
- June 2023, AS Further Pure 1, Q3 (5 marks): The rectangular hyperbola H has equation xy = c 2 where c is a positive constant. The line l has equation x – 2y = c The points P and Q are the points of inters
- June 2023, AS Further Pure 1, Q6 (8 marks): The parabola C has equation y 2 = 4ax where a is a positive constant. The point P(at 2, 2at) , t ≠ 0, lies on C The normal to C at P is parallel to the line wit
- June 2022, Further Pure 1, Q5 (9 marks): The rectangular hyperbola H has equation xy = 36 (a) Use calculus to show that the equation of the tangent to H at the point P 6 6 t t , is yt 2 + x = 12t (3
- June 2022, AS Further Pure 1, Q4 (9 marks): The parabola C has equation y2 = 10x The point F is the focus of C. (a) Write down the coordinates of F. (1) The point P on C has y coordinate q , where q > 0 (
- 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, Q7 (14 marks): The points P(9p2, 18p) and Q(9q2, 18q) , p ≠ q , lie on the parabola C with equation y2 = 36x The line l passes through the points P and Q (a) Show that an equa
- November 2020, AS Further Pure 1, Q4 (7 marks): y P O S x C Figure 2 Figure 2 shows a sketch of the parabola C with equation y2 = 4ax, where a is a positive constant. The point S is the focus of C and the poi
- June 2019, Further Pure 1, Q4 (8 marks): The parabola C has equation y 2 = 16x The distinct points P( p2, 4p) and Q(q2, 4q) lie on C, where pq The tangent to C at P and the tangent to C at Q
- June 2019, AS Further Pure 1, Q5 (10 marks): A B x y O l R P H Figure 2 Figure 2 shows a sketch of part of the rectangular hyperbola +with equation xy c x = > 2 0 where c is a positive constant. The point
- June 2018, AS Further Pure 1, Q5 (10 marks): The rectangular hyperbola H has equation xy = c2, where c is a non-zero constant. The point P cp c p p H , ≠ , where , lies on . 0 (a) Use calculus to
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