Rewrite the hyperbolic equation 4y^2 -9x^2 +54x-8y-113=0

Standard form:

(1/9)(y - 1)^2 - (1/4)(x - 3)^2 = 1

Step-by-step explanation:

4y^2 -9x^2 +54x-8y-113=0

-9(x^2 - 6x) + 4(y^2 - 2y) - 113 = 0

Completing the square:-

-9 [(x - 3)^2 - 9] + 4 [ y - 1)^2 - 1] = 113

-9(x - 3)^2 + 81 + 4(y - 1)^2 - 4 =  113

-9(x - 3)^2 + 4(y - 1)^2  =  113 - 77

-9(x - 3)^2 + 4(y - 1)^2 = 36.

Divide through by 36:-

(1/9)(y - 1)^2 - (1/4)(x - 3)^2 = 1.