Answer
Parabola
The directrix is parallel to the polar axis at a distance of 3 units below the pole.
Work Step by Step
We are given the equation in polar coordinates:
$r=\dfrac{3}{1-\sin\theta}$
The equation is in the form:
$r=\dfrac{ep}{1-e\sin\theta}$
Identify $e$ from the denominator, then $p$ from the numerator:
$e=1$
$ep=3\Rightarrow (1)p=3\Rightarrow p=3$
Because $e=1$, the conic is a parabola. The directrix is parallel to the polar axis at a distance of 3 units below the pole.
