Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 55

The conic section is a hyperbola. directrix: $x=2$ eccentricity: $e=4$

Comparing the given equation with the standard form $$ r=\frac{e d}{1+e \cos \theta}. $$ We get $$ed=8, e=4.$$ We solve for $d$: $d=\frac{8}{4}=2$ Thus, we see that the directrix is: $x=2$ Since $e\gt 1$, then the conic section is a hyperbola.