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