A circle \(C _ { 1 }\) has cartesian equation \(x ^ { 2 } + ( y - 6 ) ^ { 2 } = 36\). Show that the polar equation of \(C _ { 1 }\) is \(r = 12 \sin \theta\).
A curve \(C _ { 2 }\) with polar equation \(r = 2 \sin \theta + 5,0 \leqslant \theta \leqslant 2 \pi\) is shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{b572aeb5-bcbb-4d50-964c-7f37e223f51d-5_545_837_559_651}
Calculate the area bounded by \(C _ { 2 }\).
The circle \(C _ { 1 }\) intersects the curve \(C _ { 2 }\) at the points \(P\) and \(Q\). Find, in surd form, the area of the quadrilateral \(O P M Q\), where \(M\) is the centre of the circle and \(O\) is the pole.
(6 marks)