Answer
$$r = \frac {18}{1 - 3sin(\theta)}$$
Work Step by Step
1. Determine the equation that we are going to use:
$$r = -6csc(\theta) = -6 \frac 1 {sin(\theta)} \longrightarrow rsin(\theta) = -6 \longrightarrow y = -6$$
Since the directrix is defined by $y = -6$, we are going to use $sin(\theta)$ in the equation. Since $-6$ is negative, the equation will have "$-sin(\theta)$":
$$r = \frac{ed}{1 - esin(\theta)}$$
2. Substitute the given values for $d$ (directrix) and e (eccentricity):
(d = 6)
$$r = \frac{3 (6)}{1 - 3sin(\theta)} = \frac {18}{1 - 3sin(\theta)}$$
