8 The polar equation of a curve \(C\) is
$$r = 5 + 2 \cos \theta , \quad - \pi \leqslant \theta \leqslant \pi$$
- Verify that the points \(A\) and \(B\), with polar coordinates ( 7,0 ) and ( \(3 , \pi\) ) respectively, lie on the curve \(C\).
- Sketch the curve \(C\).
- Find the area of the region bounded by the curve \(C\).
- The point \(P\) is the point on the curve \(C\) for which \(\theta = \alpha\), where \(0 < \alpha \leqslant \frac { \pi } { 2 }\). The point \(Q\) lies on the curve such that \(P O Q\) is a straight line, where the point \(O\) is the pole. Find, in terms of \(\alpha\), the area of triangle \(O Q B\).