What is the equation of a circle?

The general equation of a circle in the Cartesian coordinate system is (x-a)² + (y-b)² = r². The point (a,b) represents the center of the circle and the value of r represents the radius of the circle.

Mathematicians can also describe a circle in the polar coordinate system by the general equation a² = r² + 2rRcos(theta-phi) + R², where the point (R,phi) represents the center of the circle in polar coordinates and the value of a represents the radius of the circle. When solved for the variable r, this equation can be rewritten as r = Rcos(theta-phi) + (a²-(sin(theta-phi))²)^1/2.