Solution
We are given
[tex]\begin{gathered} Foci=(-4,-3),(-4,7) \\ Vertices=(-4,-1),(-4,5) \\ From\text{ the above information} \\ a=3 \\ c=\frac{7-(-3)}{2}=5 \\ b^2=c^2-a^2=5^2-(3)^2 \\ b^2=25-9 \\ b^2=16 \\ b=4 \\ centre=(\frac{-4-4}{2},\frac{-3+7}{2}) \\ centre=(-4,2) \\ Equation\text{ of hyperbola} \\ \frac{(y-2)^2}{9}-\frac{(x+4)^2}{16}=1 \end{gathered}[/tex]