Answer
$r=\dfrac{4}{1+2\cos \theta}$; equation of a hyperbola
Work Step by Step
The polar equation of a conic with eccentricity $e$ and directrix $x=k$ is written as:
$r=\dfrac{ke}{1+e \cos \theta}$
Here, the vertices are: $e=2,k=2$
This gives $x=k=2$
Then, $r=\dfrac{ke}{1+e \cos \theta}=\dfrac{4}{1+2\cos \theta}$
This represents an equation of a hyperbola.
