Answer
$$r = \frac{3}{1 - cos(\theta)}$$
Work Step by Step
1. Determine the equation that we are going to use:
Since the directrix is defined by $x = -3$, we are going to use $cos(\theta)$ in the formula.
Since $-3$ is negative, the equation will have "$-cos(\theta)$":
$$r = \frac{ed}{1 - ecos(\theta)}$$
2. Substitute the given values for $d$ (directrix) and e (eccentricity):
** Notice: For parabolas: $e = 1$.
** We use the absolute value for $d$, which is $3$.
$$r = \frac{(1)(3)}{1 - (1)cos(\theta)} = \frac{3}{1 - cos(\theta)}$$
