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).

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  1. The transverse axis is vertical. You have
    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

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