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)