Answer
a. hyperbola.
b. $x=3$
Work Step by Step
a. Rewrite the given equation as $r=\frac{6}{1+2cos\theta}$ and compare with the standard form. We have $e=2, ep=6, p=3$, and we can identify the conic section as a hyperbola.
b. We can identify the location of the directrix as $x=3$ or $3$ units to the right of the pole.
