We have that
4x² − 9y²<span> − 16x − 36y − 56 = 0
</span>
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(4x² -16x) +(− 9y²− 36y)= 56
(4x² -16x) -(9y²+36y)= 56
Factor the leading coefficient of each expression
4(x²-4x) -9(y²+4y)= 56
Complete the square twice. Remember to balance the equation
by adding the same constants to each side.
4(x²-4x+4) -9(y²+4y+4)= 56+16-36
4(x²-4x+4) -9(y²+4y+4)= 36
Rewrite as perfect squares
4(x-2)² -9(y+2)²= 36
divide by 36 both sides
![[(1/9)( x-2)^{2}]-[(1/4)( y+2)^{2}]=1](https://tex.z-dn.net/?f=%5B%281%2F9%29%28%20x-2%29%5E%7B2%7D%5D-%5B%281%2F4%29%28%20y%2B2%29%5E%7B2%7D%5D%3D1)
the answer is
The equation of the hyperbola in the standard form is
![[(1/9)( x-2)^{2}]-[(1/4)( y+2)^{2}]=1](https://tex.z-dn.net/?f=%5B%281%2F9%29%28%20x-2%29%5E%7B2%7D%5D-%5B%281%2F4%29%28%20y%2B2%29%5E%7B2%7D%5D%3D1)