EQUATION: x^2 - 2x + y^2 + 6y - 6 = 0
STEP 1: x^2 - 2x + y^2 + 6y = 6
STEP 2: x^2 - 2x + [1] + y^2 + 6y + 9 = 6 + 1 + 9
So far you are correct. Now you have to factor the quadratic in x and the quadratic in y.
(x - 1)^2 + (y + 3)^2 = 16
(x - 1)^2 + (y + 3)^2 = 4^2
Compare your equation with the standard equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
Your circle is centered at (1, -3) and radius 4.
