Question: Concern C, the circle r = 2a cos θ, for -π/2 ≤ θ ≤ π/2, of radius a > 0 centered at the point (x, y)=(a, 0) on the x-axis.
1. By converting to Cartesian coordinates, show that r = 2a cos θ gives the circle described.
2. Find the area of the circle C by integrating in polar coordinates.