Chapter 11.6, Problem 40E

(a)

To determine

To find: The eccentricity and directrix of the given conic $r=\frac{9}{2+2\cos \theta }$.

(b)

To determine

To write: The resulting equation when the conic $r=\frac{9}{2+2\cos \theta }$ rotates through an angle $\theta =-\frac{5\pi }{6}$.

(c)

To determine

To sketch: The graph of the original conic $r=\frac{9}{2+2\cos \theta }$ and the rotated conic $r=\frac{9}{2+2\cos \left(\theta +\frac{5\pi }{6}\right)}$ on the same screen.