Answer
$r=\frac{3}{2-3 cos\theta}$
Work Step by Step
Given a hyperbola ($e=\frac{3}{2}$) with focus at the pole and directrix as $x=-1$, we have $p=1$ on the left side of the pole, and we can write the equation as: $r=\frac{ep}{1-e\ cos\theta}=\frac{\frac{3}{2}(1)}{1-\frac{3}{2} cos\theta}$ or $r=\frac{3}{2-3 cos\theta}$
