## Precalculus (10th Edition)

We are given the equation in polar coordinates: $r=\dfrac{2}{1+2\cos\theta}$ The equation is in the form: $r=\dfrac{ep}{1+e\cos\theta}$ Identify $e$ from the denominator, then $p$ from the numerator: $e=2$ $ep=2\Rightarrow 2p=2\Rightarrow p=1$ Because $e>1$, the conic is a hyperbola. The directrix is perpendicular to the polar axis at a distance of one unit to the right of the pole.