Answer
hyperbola with directrix perpendicular to the polar axis and 1 unit(s) to the right of the pole.
See graph.
Work Step by Step
1. Given $r=\frac{8}{4+8cos\theta}=\frac{2}{1+2cos\theta}$, compared with a standard form, we have $e=2, p=1$
2. We can identify that it is a hyperbola with directrix perpendicular to the polar axis and 1 unit(s) to the right of the pole.
3. See graph.
