5 Fig. 5 shows the curve with polar equation \(r = a ( 3 + 2 \cos \theta )\) for \(- \pi \leqslant \theta \leqslant \pi\), where \(a\) is a constant.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c2be8838-50ec-4e82-b203-4608ab56c110-3_607_718_351_244}
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{figure}
- Write down the polar coordinates of the points A and B .
- Explain why the curve is symmetrical about the initial line.
- In this question you must show detailed reasoning.
Find in terms of \(a\) the exact area of the region enclosed by the curve.