All i need is an equation of the hyperbola.

given that the center is at (2, -3), the vertices are at (2, 3) and (2, - 9), and the foci are at (2, -3 ± 2√10).

The transverse axis is vertical. You have

a=6
c=2√10
so, b^2 = c^2-a^2 = 40-36 = 4, so b=2

Thus , the equation is
(y+3)^2/36 - (x-2)^2/4 = 1