## Precalculus (6th Edition) Blitzer

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.