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:

Why the Equation of a Circle Works

The slider below explains the equation of a circle.

Open the slider in a new tab

See Also

What is an equation? What is a circle? What are Cartesian coordinates? What is the x-coordinate? What is the y-coordinate?