7 A curve \(C\) has polar equation $$r = 6 + 4 \cos \theta , \quad - \pi \leqslant \theta \leqslant \pi$$ The diagram shows a sketch of the curve \(C\), the pole \(O\) and the initial line.
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1. Calculate the area of the region bounded by the curve \(C\).
2. The point \(P\) is the point on the curve \(C\) for which \(\theta = \frac { 2 \pi } { 3 }\). The point \(Q\) is the point on \(C\) for which \(\theta = \pi\).
   Show that \(Q P\) is parallel to the line \(\theta = \frac { \pi } { 2 }\).
3. The line \(P Q\) intersects the curve \(C\) again at a point \(R\). The line \(R O\) intersects \(C\) again at a point \(S\).
   1. Find, in surd form, the length of \(P S\).
   2. Show that the angle \(O P S\) is a right angle.