Answer
See below
Work Step by Step
A hyperbola with foci $(0, \pm 5)$ and vertices on the y-axis:
Since the vertices are at $(0,\pm 2) \rightarrow a=2$.
The foci are at $(0,\pm 5) \rightarrow ae=5$.
Rewrite the equation in standard form: $\frac{x^2}{5^2-2^2}-\frac{y^2}{2^2}=1\\\frac{x^2}{21}-\frac{y^2}{4}=-1\\\frac{y^2}{4}-\frac{x^2}{21}=1$
