Answer
$r=\dfrac{2}{1+\sin \theta}$
Work Step by Step
The equation of conic with eccentricity $e$ and directrix $x=k$ leads to focus can be written as:
$r=\dfrac{ke}{1+e \cos \theta}$
Given: $e=1,k=2$
Then $x=2$
Then, the equation (1) can be written as:
$r=\dfrac{ke}{1+e \cos \theta}=\dfrac{(2)(1)}{1+(1) \sin \theta}$
Thus, $r=\dfrac{2}{1+\sin \theta}$
