Substitute back: $ 9(x - 2)^2 - 36 - 4(y - 3)^2 + 36 = 36 $. Simplify: $ 9(x (x - 2)^2 - 4) - 4(y - 3)^2 = 36 $. Divide by 36: $ \frac(x - 2)^24 - \frac(y - 3)^29 = 1 $. The center is at $ (2, 3) $. The center is $\boxed(2, 3)$. - go-checkin.com