Step 1 :Rewrite the given equation by completing the square for both x and y terms: \( (x^2 - 2x + 1) + (y^2 - 12y + 36) = 11 + 1 + 36 \)
Step 2 :Simplify the equation: \( (x - 1)^2 + (y - 6)^2 = 48 \)
Step 3 :The center of the circle is \( \boxed{(1, 6)} \)