Answer
$IV$
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 $e=1$
When we look at all the graphs it has been noticed when $e=\dfrac{2}{3} \lt 1$ . This shows that the conic is an ellipse, so the correct graph is $IV$.
