4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{04f06398-ff29-4690-a6fe-825d089fba39-05_663_665_228_644}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\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
- write down the length of \(P Q\).
Given that the point \(P\) has \(x\) coordinate 9
find - the value of \(a\),
- the area of triangle \(P S Q\).