| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola tangent equation derivation |
| Difficulty | Standard +0.3 This is a straightforward Further Maths parabola question using parametric coordinates. Part (a) requires standard implicit differentiation or parametric differentiation to find the tangent equation—a routine technique. Part (b) is even simpler, requiring only substitution of the new parameter into the formula derived in part (a). While it's Further Maths content, the execution is mechanical with no problem-solving insight needed. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07m Tangents and normals: gradient and equations |
The point $P(ap^2, 2ap)$ lies on the parabola $M$ with equation $y^2 = 4ax$, where $a$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Show that an equation of the tangent to $M$ at $P$ is $py = x + ap^2$. [3]
\end{enumerate}
The point $Q(16ap^2, 8ap)$ also lies on $M$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Write down an equation of the tangent to $M$ at $Q$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q25 [5]}}