9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7833e9c0-4a73-4ac6-8a77-51a5489e0614-10_624_716_210_614}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the parabola with equation \(y ^ { 2 } = 36 x\).
The point \(P ( 4,12 )\) lies on the parabola.
- Find an equation for the normal to the parabola at \(P\).
This normal meets the \(x\)-axis at the point \(N\) and \(S\) is the focus of the parabola, as shown in Figure 1.
- Find the area of triangle \(P S N\).