Answer
hyperbola directrix is perpendicular to the polar axis, $1$ unit to the right the pole.
Work Step by Step
Given $r=\frac{2}{1+2cos\theta}$, we have $e=2\gt1$, thus it is a hyperbola. From the equation and with the $cos\theta$ term, we know $p=1$ and the directrix is perpendicular to the polar axis, $1$ unit to the right the pole.
