Answer
$\dfrac{4}{1+2\cos \theta}$; equation of a hyperbola
Work Step by Step
The polar equation of a conic with eccentricity $e$ and directrix $x=k$ is:
$r=\dfrac{ke}{1+e \cos \theta}$ ...(1)
We are given that the vertices are: $e=2,k=2$
Then $x=2$
Thus, equation (1), becomes
$r=\dfrac{4}{1+2\cos \theta}$; equation of a hyperbola
