8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{18620cc5-2377-480b-b815-63bfc6a9760a-15_618_942_255_584}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The curve \(C _ { 1 }\) with equation
$$r = 7 \cos \theta , \quad - \frac { \pi } { 2 } < \theta \leqslant \frac { \pi } { 2 }$$
and the curve \(C _ { 2 }\) with equation
$$r = 3 ( 1 + \cos \theta ) , \quad - \pi < \theta \leqslant \pi$$
are shown on Figure 1.
The curves \(C _ { 1 }\) and \(C _ { 2 }\) both pass through the pole and intersect at the point \(P\) and the point \(Q\).
- Find the polar coordinates of \(P\) and the polar coordinates of \(Q\).
The regions enclosed by the curve \(C _ { 1 }\) and the curve \(C _ { 2 }\) overlap, and the common region \(R\) is shaded in Figure 1.
- Find the area of \(R\).