Equation of a Circle in the Coordinate Plane

The equation of a circle with center (h, k) and radius r: [formula] Examples: - Center (3, -2), radius 5: (x-3)^2 + (y+2)^2 = 25 - Center at origin, radius 4: x^2 + y^2 = 16 General form: x^2 + y^2 + Dx + Ey + F = 0. To find center and radius, complete the square.

Example: Write the equation: x^2 + y^2 - 6x + 4y - 12 = 0 in standard form.

To complete the square for x^2 + bx: take half of b, square it, and add it to both sides. For x^2 - 6x: half of -6 is -3, squared is 9. So add 9.