Answer
ellipse; see graph.
Work Step by Step
Step 1. Rewrite the given equation in standard form as $r=\frac{16}{4-3cos\theta}=\frac{4}{1-\frac{3}{4}cos\theta}$
Step 2. We can identify: $e=\frac{3}{4}\lt 1$, representing an ellipse.
Step 3. We can identify: $ep=4, p=\frac{16}{3}$ and the directrix as $x=-\frac{16}{3}$
Step 4. We can graph the equation as shown in the figure.
