Chapter 11.6, Problem 39E

(a)

To determine

To find: The eccentricity and directrix of the given conic $r=\frac{2}{1+\sin \theta }$.

(b)

To determine

To write: The resulting equation when the conic $r=\frac{2}{1+\sin \theta }$ rotates through an angle $\theta =-\frac{\pi }{4}$.

(c)

To determine

To sketch: The graph of the conic $r=\frac{2}{1+\sin \theta }$ and its rotated conic $r=\frac{2}{1+\sin \left(\theta +\frac{\pi }{4}\right)}$ on the same screen.