Answer
ellipse, see graph
Work Step by Step
Step 1. Rewrite the equation as
$r=\frac{4/cos\theta}{2/cos\theta-1}=\frac{4}{2-cos\theta}=\frac{2}{1-\frac{1}{2}cos\theta}$
Step 2. We can identify $e=\frac{1}{2}\lt 1$ and the conic is an ellipse with $ep=2, p=4$ and directrix as $x=-4$
Step 3. We can graph the equation as shown in the figure.
