Equation of a Circle
Equation of a circle with centre (a,b) and radius r.



PR = x - a, PQ = r

QR = y - b

Since ΔPQR is the right angle triangle, we have: PQ2 = PR2 + QR2

r2 = (x - a)2 + (y - b)2

if the center of the circle is the origin (0, 0), the equation becomes x2 + y2 = r2

General Equation of a Circle

From (x - a)2 + (y - b)2 = r2

r2 - 2ax + a2 + y2 - 2by + b2 - r2 = 0

x2 + y2 - 2ax - 2by + a2 + b2 - r2 = 0

The above equation can be written as x2 + y2 + 2gx + 2fy + c = 0

Where a = -g, b = -f, c = -a2 + b2 - r2

Hence: x2 + y2 + 2gx + 2fy + c = 0 is called the general equation of a circle.