FP2 polar coordinates

The curve C has polar equation r = 3a cos θ , -π/2 ≤ θ ≤ π/2
The curve D has polar equation r = a(1 + cos θ ), -π ≤ θ ≤ π
Given that a is a positive constant,

(a) sketch, on the same diagram, the graphs of C and D, indicating where each curve cuts the initial line.


The graphs of C intersect at the pole O and at the points P and Q.

(b) Find the polar coordinates of P and Q.

(c) Use integration to find the exact value of the area enclosed by the curve D and the lines θ = 0 and θ = π/3

The region R contains all points which lie outside D and inside C.

Given that the value of the smaller area enclosed by the curve C and the line θ = π/3 is

3a²/16(2π - 3√3),

(d) show that the area of R is πa².