Consider the polar curve given by r=4cosθ.
(a) Rewrite the equation of the curve in rectangular coordinates and simplify completely.
(b) Identify the center, radius, and orientation of the curve you obtained in part (a), and describe the portion of the plane it occupies.
(c) For 0≤θ≤2π, the curve encloses a region S. Explain, without performing any integration, why S must represent exactly one–quarter of the full region bounded by the curve.