Answer
parabola, see graph
Work Step by Step
Step 1. Rewrite the given equation in standard form as
$r=\frac{18}{6-6cos\theta}=\frac{3}{1-cos\theta}$
Step 2. We can identify: $e=1$, representing a parabola.
Step 3. We can identify: $ep=3, p=3$ and the directrix as $x=-3$
Step 4. We can graph the equation as shown in the figure.
