Answer
ellipse, directrix is perpendicular to the polar axis, $\frac{3}{2}$ units to the left the pole.
Work Step by Step
Given $r=\frac{3}{4-2cos\theta}=\frac{3/4}{1-\frac{1}{2}cos\theta}$, we have $e=\frac{1}{2}\lt1$, thus it is an ellipse. From the equation and with the $-cos\theta$ term, we know $p=\frac{3}{2}$ and the directrix is perpendicular to the polar axis, $\frac{3}{2}$ units to the left the pole.
