Answer
\[\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1,\text{ where }{{b}^{2}}={{c}^{2}}-{{a}^{2}}\]
Work Step by Step
\[\begin{align}
& \text{The equation of the standard hyperbola with vertices at }\left( 0,\pm a \right) \\
& \text{and foci at }\left( 0,\pm c \right)\text{ is:} \\
& \frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1,\text{ where }{{b}^{2}}={{c}^{2}}-{{a}^{2}} \\
\end{align}\]
