Answer
See explanations.
Work Step by Step
From the given equation, convert it to the standard form of $r=\frac{ep}{1\pm e\ sin\theta}$ or $r=\frac{ep}{1\pm e\ cos\theta}$. We can then find the values of $e$ and $p$. The location of the directrix will be $p$ units away from the focus at the pole and its orientation and relative position (left, right, above, below) from the focus will depend on the $\pm$ signs and $sin$ or $cos$ used in the equation.
