6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d20fa710-2d91-4ac2-adbc-46ccdcb93380-07_789_791_228_566}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the parabola \(C\) with equation \(y ^ { 2 } = 36 x\). The point \(S\) is the focus of \(C\).
- Find the coordinates of \(S\).
- Write down the equation of the directrix of \(C\).
Figure 1 shows the point \(P\) which lies on \(C\), where \(y > 0\), and the point \(Q\) which lies on the directrix of \(C\). The line segment \(Q P\) is parallel to the \(x\)-axis.
Given that the distance \(P S\) is 25 ,
- write down the distance \(Q P\),
- find the coordinates of \(P\),
- find the area of the trapezium \(O S P Q\).