Answer
$\displaystyle \frac{y^{2}}{25}-\frac{x^{2}}{9}=1$
Work Step by Step
The branches of the graph indicate that
the transverse axis is vertical,
the center is at the origin, so
the form of the equation is $\displaystyle \frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1$
From the graph,
$a=5,$
$b=3$.
$\displaystyle \frac{y^{2}}{25}-\frac{x^{2}}{9}=1$