Precalculus (6th Edition) Blitzer

Given a polar equation of the general form $r=\frac{a}{b+c\ sin\theta}$ or $r=\frac{a}{b+c\ cos\theta}$, divide $b$ from both the numerator and the denominator. We have $r=\frac{a/b}{1+c/b\ sin\theta}$ or $r=\frac{a/b}{1+c/b\ cos\theta}$. We can find the eccentricity as $e=\frac{c}{b}$.