Answer
$r=\frac{12}{5-4\ cos\theta}$.
Work Step by Step
1. Based on the given direction and position of the directrix, we know the equation has a form
$r=\frac{ep}{1-e\ cos\theta}$,
2. With $e=\frac{4}{5}$ and $p=3$, we have $r=\frac{12/5}{1-\frac{4}{5}cos\theta}=\frac{12}{5-4\ cos\theta}$.
