7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{84aadcb2-399f-4168-94c6-4e6ed0450d6d-12_866_1026_274_468}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curves \(C _ { 1 }\) and \(C _ { 2 }\) with polar equations
$$\begin{array} { l l }
C _ { 1 } : r = \frac { 3 } { 2 } \cos \theta , & 0 \leqslant \theta \leqslant \frac { \pi } { 2 }
C _ { 2 } : r = 3 \sqrt { 3 } - \frac { 9 } { 2 } \cos \theta , & 0 \leqslant \theta \leqslant \frac { \pi } { 2 }
\end{array}$$
The curves intersect at the point \(P\).
- Find the polar coordinates of \(P\).
The region \(R\), shown shaded in Figure 1, is enclosed by the curves \(C _ { 1 }\) and \(C _ { 2 }\) and the initial line.
- Find the exact area of \(R\), giving your answer in the form \(p \pi + q \sqrt { 3 }\) where \(p\) and \(q\) are rational numbers to be found.