Algebra questions

Question

The hyperbola is given by equation

4x² – 9y² + 32x + 54y – 53 = 0.

Find the coordinates of the center, the foci, the eccentricity and the asymptotes of the hyperbola.

Answer 1

4x^2+32x+64-9y^2+54x-81 = 53+64-81 = 36

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

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

(-4,3)