Answer
$$\frac{{{y^2}}}{{49}} - \frac{{{x^2}}}{{392}} = 1$$
Work Step by Step
$$\eqalign{
& {\bf{e}} = 3;{\text{ center at }}\left( {0,0} \right);{\text{ vertex at }}\left( {0,7} \right) \cr
& {\text{The }}x{\text{ - coordinate in the vertex and center are the same, then }} \cr
& {\text{the hyperbola has the equation }}\frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}} = 1 \cr
& {\text{vertices at }}\left( {0, \pm a} \right){\text{,}}\,{\text{ vertex at }}\left( {0,7} \right) \cr
& a = 7 \cr
& \cr
& {\text{excentricity }}{\bf{e}} = \frac{c}{a} \cr
& 3 = \frac{c}{7} \cr
& c = 21 \cr
& {b^2} = {21^2} - {7^2} \cr
& {b^2} = 392 \cr
& \cr
& {\text{The equation of the hyperbola is}} \cr
& \frac{{{y^2}}}{{49}} - \frac{{{x^2}}}{{392}} = 1 \cr} $$
