Edexcel FP2 2016 June — Question 8

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2016
SessionJune
TopicPolar coordinates

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 \(Q\).
  1. 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.
  2. Find the area of \(R\).