Chapter 10 - Section 10.6 - Conic Sections in Polar - 10.6 Exercises - Page 717: 10

Graph III

Find $e$ and $d$: $r=\frac{9}{1+2\cos\theta}$ $\frac{ed}{1+e\cos\theta}=\frac{9}{1+2\cos\theta}$ $e=2$ and $ed=9$ $e=2$ and $d=\frac{9}{2}$ Using Theorem 6, and using part (a) of Figure 2, the given polar equation represents a horizontal hyperbola with the eccentricity $2$ and the directrix $x=\frac{9}{2}$. It is shown in Graph III.