# How do you write a standard form equation for the hyperbola with 9x^2-100y^2+18x+600y+9=0?

Nov 17, 2015

Simply complete the square for both the x and y variables.

#### Explanation:

First, group together by variable and simplify:

$9 \left({x}^{2} + 2 x\right) - 100 \left({y}^{2} - 6 y\right) = - 9$

Next, complete the squares, but be sure to keep both sides of the equation balanced!

$9 \left({x}^{2} + 2 x\right) - 100 \left({y}^{2} - 6 y\right) = - 9$

$9 \left({x}^{2} + 2 x + 1\right) - 100 \left({y}^{2} - 6 y + 9\right) = - 9 + 9 - 900$

$9 {\left(x + 1\right)}^{2} - 100 {\left(y - 3\right)}^{2} = - 900$

Finally, divide by -900

${\left(y - 3\right)}^{2} / 9 - {\left(x + 1\right)}^{2} / 100 = 1$

So, this is a hyperbola with center $C = \left(- 1 , 3\right)$

hope that helped