The general equation of the circle is

x2 + y2 + 2gx + 2fy + c = 0

The equation represents a circle with

Centre = (−g, −f)

Radius = √(g2 + f2 − c)

The general second degree equation

ax2 + by2 + 2hxy + 2gx + 2fy + c = 0

represents a circle if

  1. a = b (coefficient of x2 = coefficient of y2)
  2. h = 0 (no xy term)