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)^2}{4} - \frac{(y - 3)^2}{9} = 1 $. The center is at $ (2, 3) $. The center is $\boxed{(2, 3)}$.