Answer
$$\frac{{{y^2}}}{{36}} - \frac{{{x^2}}}{{64}} = 1$$
Work Step by Step
$$\eqalign{
& {\text{From the graph we can see that the orientation of the transverse}} \cr
& {\text{axis is vertical }}\left( {{\text{along the y - axis}}} \right){\text{ and the hyperbola is centered }} \cr
& {\text{at the Origin}}.{\text{ Then, the equation is of the form}} \cr
& \frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}} = 1 \cr
& and \cr
& {\text{Vertices }}\left( {0, \pm a} \right),\,\,{\text{foci }}\left( {0, \pm c} \right) \cr
& {\text{Vertices }}\left( {0, \pm 6} \right),\,\,{\text{foci }}\left( {0, \pm 10} \right) \cr
& a = 6,\,\,\,c = 10 \cr
& b = \sqrt {{c^2} - {a^2}} = \sqrt {100 - 36} = 8 \cr
& \cr
& {\text{The equation of the hyperbola is}} \cr
& \frac{{{y^2}}}{{{6^2}}} - \frac{{{x^2}}}{{{8^2}}} = 1 \cr
& \frac{{{y^2}}}{{36}} - \frac{{{x^2}}}{{64}} = 1 \cr} $$
