Question

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

Answer 1

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