Answer
$x=\dfrac{1}{8}(y-2)^2+1$
Work Step by Step
General form of a horizontal parabola is given as: $(y-k)^2=4p(x-h)$...(1)
Here, $\text{Vertex}=(h,k)$ and focus is: $(h+p, k)$
General form of a vertical parabola is given as: $(x-h)^2=4p(y-k)$...(2)
Here, $\text{Vertex}=(h,k)$ and focus is: $(h, k+p)$
As we are given focus: $(3,2)$
Thus, from both forms of a parabola , we have two equations$h-p=-1$ and $h+p=3$
Add these two equations, we get: $h=1$
Thus, $p=3-h=3-1=2$
From equation (1), we have $(y-2)^2=4(2)(x-1)$
or, $(y-2)^2=8(x-1)$
or, $x-1=\dfrac{(y-2)^2}{8}$
or, $x=\dfrac{1}{8}(y-2)^2+1$
