Chapter 11.6, Problem 37E

(a)

To determine

To find: The eccentricity and directrix of the conic $r=\frac{1}{4-3\cos \theta }$.

(b)

To determine

To write: The resulting equation when the conic $r=\frac{1}{4-3\cos \theta }$ rotates through an angle $\theta =\frac{\pi }{3}$.

(c)

To determine

To draw: The graph of the original conic $r=\frac{1}{4-3\cos \theta }$ rotated conic

$r=\frac{1}{4-3\cos \left(\theta -\frac{\pi }{3}\right)}$ on the same screen.