What Is the Equation of a Circle (Not Centered at the Origin)?
What Is the Equation of a Circle (Not Centered at the Origin)?
The equation of a circle, with a center with Cartesian coordinates (a, b) is in the form:
In this equation,

x and y are the Cartesian coordinates of points on the (boundary of the) circle.

a and b are the Cartesian coordinates of the center of the circle.

r is the radius of the circle.
The image below shows what we mean by a point on a circle centered at (a, b) and its radius:
Real Examples of Equations of Circles (Not Centered on the Origin)
It is easier to understand the equation of a circle with examples.

A circle centered at (2, 3) with a radius of 5 will have the equation:

A circle centered at (−1, 1) with a radius of 3 will have the equation: