Answer
$\dfrac{y^2}{25}-\dfrac{x^2}{9}=1$
Work Step by Step
Center: $(0,0)$ and vertices: $(0,-5); (0,5)$
This yields: $ a=2$ and Asymptote: $ y=\dfrac{5}{3} x \implies b=3$
And we have a vertical traverse axis.
Standard Equation for a hyperbola is : $\dfrac{y^2}{a^2}-\dfrac{x^2}{b^2}=1$
We have $ a^2=25; b^2 =9$
So, the equation for the hyperbola is:
$\dfrac{y^2}{25}-\dfrac{x^2}{9}=1$
