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