Convert the equation to the standard form for a hyperbola 4x^2-25y^2-8x+50y-121=0

We have that

4x²-25y² - 8x+50y-121=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(4x²-8x) + (-25y²+50y) = 121

Factor the leading coefficient of each expression

4 (x²-2x) - 25 (y²-2y) = 121

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

4 (x²-2x+1) ²-25 (y²-2y+1) ²=121+4-25

Rewrite as perfect squares

4 (x-1) ²-25 (y-1) ²=100

Divide both sides by the constant term to place the equation in standard form

(4/100) (x-1) ² - (25/100) (y-1) ²=100/100

(1/25) (x-1) ² - (1/4) (y-1) ²=1

[ (x-1) ²]/25-[ (y-1) ²]/4=1

the answer is

[ (x-1) ²]/25-[ (y-1) ²]/4=1