Given:

\[Vertices\text{ }\left( 0,~\pm ~3 \right)\text{ }and\text{ }foci\text{ }\left( 0,~\pm ~5 \right)\]

Here, the vertices are on the$y-axis$.

Along these lines, the condition of the hyperbola is of the structure \[{{y}^{2}}/{{a}^{2}}~\text{ }{{x}^{2}}/{{b}^{2}}~=\text{ }1\]

Since, the vertices are \[\left( 0,~\pm 3 \right),\]along these lines, \[a\text{ }=\text{ }3\]

Since, the foci are \[~\left( 0,~\pm 5 \right),\]in this way, \[c\text{ }=\text{ }5\]

It is realize that, \[{{a}^{2}}~+\text{ }{{b}^{2}}~=\text{ }{{c}^{2}}\]

In this way, \[{{3}^{2}}~+\text{ }{{b}^{2}}~=\text{ }{{5}^{2}}\]

\[{{b}^{2}}~=\text{ }25\text{ }\text{ }9\text{ }=\text{ }16\]

∴ The condition of the hyperbola is \[{{y}^{2}}/9\text{ }\text{ }{{x}^{2}}/16\text{ }=\text{ }1\]