Answer
parabola, directrix is parallel to the polar axis, $3$ unit(s) below the pole, vertex $(\frac{3}{2},\frac{3\pi}{2})$.
See graph.
Work Step by Step
1. Given $r=\frac{3}{1-sin\theta}$, we have $e=1$, thus it is a parabola. From the equation and with the $-sin\theta$ term, we know $p=3$ and the directrix is parallel to the polar axis, $3$ unit(s) below the pole, vertex $(\frac{3}{2},\frac{3\pi}{2})$
2. See graph.
