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
[tex][(1/9)( x-2)^{2}]-[(1/4)( y+2)^{2}]=1[/tex]
the answer is
The equation of the hyperbola in the standard form is
[tex][(1/9)( x-2)^{2}]-[(1/4)( y+2)^{2}]=1[/tex]
