Answer
$y=\dfrac{1}{16}(x-7)^2-5$
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: $(7,-1)$
Thus, from both forms of a parabola , we have two equations$k-p=-9$ and $k+p=-1$
Add these two equations, we get: $k=-5$
Thus, $p=-1-k=-1-(-5)=4$
From equation (1), we have $(x-7)^2=4(4)(y-(-5))$
or, $(x-7)^2=16(y+5)$
or, $y=\dfrac{1}{16}(x-7)^2-5$
