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.