8.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{858e6727-8498-462a-8064-d65254f1fd0f-04_559_954_1091_552}
\end{figure}
The curve \(C\) shown in Fig. 1 has polar equation
$$r = a ( 3 + \sqrt { 5 } \cos \theta ) , \quad - \pi \leq \theta < \pi$$
- Find the polar coordinates of the points \(P\) and \(Q\) where the tangents to \(C\) are parallel to the initial line.
(6)
The curve \(C\) represents the perimeter of the surface of a swimming pool. The direct distance from \(P\) to \(Q\) is 20 m . - Calculate the value of \(a\).
- Find the area of the surface of the pool.
(6)
[0pt]
[P4 June 2002 Qn 8]