Answer
$V$
Work Step by Step
The equation of conic with eccentricity $e$ and directrix $d=x$ leads to focus can be written as:
$r=\dfrac{d}{1 -\cos \theta}$ when $e=1$
When we look at all the graphs it has been noticed, we have $e=\dfrac{3}{2} \gt 1$ . This shows that the conic is a hyperbola, so the correct graph is $V$.
