How do you write a standard form equation for the hyperbola with 9x^2 – y^2 – 36x + 4y + 23 = 0?

Mar 20, 2016

${\left(x - 2\right)}^{2} / {1}^{2} - {\left(y - 2\right)}^{2} / {3}^{2} = 1$

Explanation:

Rewrite, the equation as follows:

$9 \left({x}^{2} - 4 x\right) - \left({y}^{2} - 4 y\right) + 23 = 0$

$9 \left({x}^{2} - 4 x + 4\right) - \left({y}^{2} - 4 y + 4\right) - 36 + 4 + 23 = 0$

#9(x-2)^2 - (y-2)^2 = 9

${\left(x - 2\right)}^{2} / {1}^{2} - {\left(y - 2\right)}^{2} / {3}^{2} = 1$