| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola focus and directrix properties |
| Difficulty | Standard +0.3 This question tests the fundamental focus-directrix property of parabolas (PS = PQ) which is definitional knowledge for Further Maths students. Parts (b) and (c) involve straightforward substitution and basic coordinate geometry calculations. While it's a Further Maths topic, the question requires only direct application of standard results with minimal problem-solving. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian |
4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{04f06398-ff29-4690-a6fe-825d089fba39-05_663_665_228_644}
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\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the parabola $C$ with equation $y ^ { 2 } = 4 a x$, where $a$ is a positive constant. The point $S$ is the focus of $C$ and the point $Q$ lies on the directrix of $C$. The point $P$ lies on $C$ where $y > 0$ and the line segment $Q P$ is parallel to the $x$-axis.
Given that the length of $P S$ is 13
\begin{enumerate}[label=(\alph*)]
\item write down the length of $P Q$.
Given that the point $P$ has $x$ coordinate 9\\
find
\item the value of $a$,
\item the area of triangle $P S Q$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2015 Q4 [6]}}