Answer
$\dfrac{5(y-4)^{2}}{16}-\dfrac{5(x-2)^{2}}{64}=1$
Work Step by Step
Asymptotes are $y=3+1/2x, y=5-1/2x$
which gives $\frac{a}{b}=\frac{1}{2}$
$2a=b$
$a^2+(2a)^2=4^2$
$a=\frac{4}{\sqrt 5}$ and $b=\frac{8}{\sqrt 5}$
The equation of the hyperbola is
$\dfrac{5(y-4)^{2}}{16}-\dfrac{5(x-2)^{2}}{64}=1$
