What Is the Equation of a Circle?

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.