| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2023 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Rectangular hyperbola tangent intersection |
| Difficulty | Challenging +1.2 This is a Further Maths question on parabola properties using parametric forms. Parts (a) and (b) are routine verification/showing exercises requiring substitution and algebraic manipulation. Part (c) requires finding tangent equations and their intersection, which is a standard technique in F1 conic sections but involves more algebraic work than typical A-level questions. The parametric approach and focus property elevate it slightly above average difficulty. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item The point $P \left( 2 p ^ { 2 } , 4 p \right)$ lies on the parabola with equation $y ^ { 2 } = 8 x$\\
(a) Show that the point $Q \left( \frac { 2 } { p ^ { 2 } } , \frac { - 4 } { p } \right)$, where $p \neq 0$, lies on the parabola.\\
(b) Show that the chord $P Q$ passes through the focus of the parabola.
\end{enumerate}
The tangent to the parabola at $P$ and the tangent to the parabola at $Q$ meet at the point $R$\\
(c) Determine, in simplest form, the coordinates of $R$
\hfill \mbox{\textit{Edexcel F1 2023 Q8 [13]}}