The curve \(C\) has polar equation \(r=3+2 \cos \theta\), for \(-\pi\lt \theta \leqslant \pi\). The straight line \(l\) has polar equation \(r \cos \theta=2\). Sketch both \(C\) and \(l\) on a single diagram.

Find the polar coordinates of the points of intersection of \(C\) and \(l\).

The region \(R\) is enclosed by \(C\) and \(l\), and contains the pole. Find the area of \(R\).
[Question 11 is printed on the next page.]