Answer
$(x+3)^2=4(y-3)$
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: $(-3,4)$
Thus, from both forms of a parabola , we have two equations$k-p=2$ and $k+p=4$
Add these two equations, we get: $k=3$
Thus, $p=4-k=4-3=1$
From equation (1), we have $(x-(-3))^2=4(1)(y-3)$
or, $(x+3)^2=4(y-3)$
