Answer
hyperbola, see graph
Work Step by Step
Step 1. Rewrite the given equation in standard form as $r=\frac{12}{4+5sin\theta}=\frac{3}{1+\frac{5}{4}sin\theta}$
Step 2. We can identify: $e=\frac{5}{4}\gt 1$, representing a hyperbola.
Step 3. We can identify: $ep=3, p=\frac{12}{5}$ and the directrix as $y=\frac{12}{5}$
Step 4. We can graph the equation as shown in the figure.
