Find, in terms of \(a\), the polar coordinates of the points where the curve \(C _ { 1 }\) meets the circle \(C _ { 2 }\).(4)
\end{enumerate}
The regions enclosed by the curves \(C _ { 1 }\) and \(C _ { 2 }\) overlap and this common region \(R\) is shaded in the figure.
Find, in terms of \(a\), an exact expression for the area of the
\includegraphics[max width=\textwidth, alt={}, center]{863ef52d-ae75-450c-9eab-8102804868f5-1_523_707_1262_1255}
region \(R\).(8)
In a single diagram, copy the two curves in the diagram above and also sketch the curve \(C _ { 3 }\) with polar equation \(r = 2 a \cos \theta , 0 \leq \theta < 2 \pi\) Show clearly the coordinates of the points of intersection of \(\mathrm { C } _ { 1 } , \mathrm { C } _ { 2 }\) and \(\mathrm { C } _ { 3 }\) with the initial line, \(\theta = 0\).(3)(Total 15 marks)