Final answer:
The equation of the circle in center-radius form is (x - 1)² + (y - 2)² = 3.
Step-by-step explanation:
The general form of a circle equation is given by x² + y² + Dx + Ey + F = 0. To convert this general form into center-radius form, we need to complete the square for both x and y. First, let's group the x and y terms together: x² - 2x + y² - 4y = -2. To complete the square for x, we take half the coefficient of x (-2), square it (-2/2)^2 = 1, and add it to both sides of the equation. Doing the same for y, we add (4/2)^2 = 4 to both sides. This gives us the equation: (x - 1)² + (y - 2)² = 3.