| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola tangent intersection problems |
| Difficulty | Standard +0.3 This is a structured multi-part question on parabola properties using parametric form. Part (a) requires implicit differentiation and substitution (standard technique), parts (b-d) involve straightforward coordinate geometry. While it's a Further Maths topic, the question guides students through each step with no novel insight required—slightly easier than average A-level difficulty overall. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
A parabola has equation $y^2 = 4ax$, $a > 0$. The point $Q (aq^2, 2aq)$ lies on the parabola.
\begin{enumerate}[label=(\alph*)]
\item Show that an equation of the tangent to the parabola at $Q$ is
$$yq = x + aq^2.$$
[4]
\item This tangent meets the $y$-axis at the point $R$.
Find an equation of the line $l$ which passes through $R$ and is perpendicular to the tangent at $Q$.
[3]
\item Show that $l$ passes through the focus of the parabola.
[1]
\item Find the coordinates of the point where $l$ meets the directrix of the parabola.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q8 [10]}}