Answer
$r =\frac{6}{3+2\ sin\theta}$.
Work Step by Step
1. Based on the given direction and position of the directrix, we know the equation has a form
$r=\frac{ep}{1+e\ sin\theta}$,
2. With $e=\frac{2}{3}$ and $p=3$, we have $r=\frac{2}{1+\frac{2}{3}\ sin\theta}=\frac{6}{3+2\ sin\theta}$.
