Answer
a. parabola.
b. $y=-4$
Work Step by Step
a. Rewrite the given equation as $r=\frac{4}{1- sin\theta}$ and compare with the standard form. We have $e=1, ep=4, p=4$, and we can identify the conic section as a parabola.
b. We can identify the location of the directrix as $y=-4$ or $4$ units below the pole.
