Chapter 10 - Section 10.6 - Conic Sections in Polar - 10.6 Exercises - Page 717: 3

$r=\frac{8}{1-2\sin\theta}$

Using Theorem 6 with $e=2$ and $d=4$, and using part (d) of Figure 2, the hyperbola with the focus at the origin, the eccentricity $2$, and the directrix $y=-4$ has the following equation: $r=\frac{2\cdot 4}{1-2\sin \theta}$ $r=\frac{8}{1-2\sin\theta}$