## Calculus (3rd Edition)

$$r=\frac{4}{1+ \cos \theta} .$$
The polar equation of a conic of eccentricity $e \gt0$, with focus at the origin and directrix $x = d$ is $$r=\frac{e d}{1+e \cos \theta}.$$ Now, since $e=1$ and $x=4$, then the polar equation is $$r=\frac{4}{1+ \cos \theta} .$$