What Is the Equation of a Circle (in General Form)?

What Is the Equation of a Circle (in General Form)?

The equation of a circle, in general form is in the form:

In this equation,

The image below shows what we mean by a point on a circle:

A Real Example of an Equation of a Circle (in General Form)

An example of an equation of a circle in general form is given below:

In this example, A = −2, B = −4 and C = −4.

We cannot directly tell any thing about this circle from this equation.

We can use completing the square to convert this equation from general form to standard form, and then find the center and radius:

x2 + y2 − 2x − 4x − 4 = 0

(x − 1)2 + (y − 2)2 = 9

This circle has center (1, 2) and radius 3.

Read more about converting an equation of a circle in general form to standard form

See Also

What is an equation? What is a circle? What are Cartesian coordinates? Completing the square