Answer
hyperbola, directrix is parallel to the polar axis, $\frac{4}{3}$ units below the pole.
Work Step by Step
Given $r=\frac{4}{2-3sin\theta}=\frac{2}{1-\frac{3}{2}sin\theta}$, we have $e=\frac{3}{2}\gt1$, thus it is a hyperbola. From the equation and with the $-sin\theta$ term, we know $p=\frac{4}{3}$ and the directrix is parallel to the polar axis, $\frac{4}{3}$ units below the pole.
