Write the standard form of the equation of the hyperbola 4x2 − 9y2 − 16x − 36y − 56 = 0.

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

the answer is

The equation of the hyperbola in the standard form is

step-by-step explanation:

in the absence of parentheses, i will have to make some assumptions:   i interpret your (3x+5/y^6)(4y^3/5)​ to mean:

3x + 5     4y^(3/5)       (3x + 5)(4)

* =

    y^6             1               y^(6-3/5)

if this is not what you expected, repost your question using parentheses to indicate whether you meant

4y^3

    or   4y^(3/5)

    5

there will be 35 boys in each team. : )