Write 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, ± 2√10).

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  1. use what you know about hyperbolas.

    Since the center and vertices are bot at x=2, the axis is vertical. So, given the center, we have

    (y+3)^2/a^2 - (x-2)^2/b^2 = 1

    However, you have garbled the foci. Since the center is at y = -3, the foci cannot be symmetric about the x-axis.

    Fix that, and then, knowing that
    a = 6
    and c = the real distance to the foci,
    and b^2 = c^2-a^2

    then you can write the equation.

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