# Circle Equation

A circle is the set of all points in a plane at a given distance, called the radius, from a given point called the center. The equation of a circle is a way to express the definition of a circle on the coordinate plane. When the center of the circle is at the point C(x_1,y_1), the equation becomes (x - x_1)^2 + (y - y_1)^2 = r^2, where r is the radius.

A circle with the equation x^2 + y^2 = 36 is a circle with its center at the origin and a radius of 6.

Created with GeoGebra by Vitor Nunes

### Interactivity

Try moving the point C (which defines the center of the circle) and change the value of r.

The circle (of brown color) defines the points of the plane that are all at the same distance from the center. This distance is r (the radius of the circle).

## Circle on a Graph

Circle equations are often found in the general form of ax^2 + by^2 + cx + dy + e = 0. Unfortunately, it can be difficult to decipher any meaningful properties about a given circle from its general equation. Using the Completing the Square technique converts the equation to an easier form, which contains values for the center and radius of the circle.