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,

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

A, B and C are constants. They have no meaning.
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:
x^{2} + y^{2} − 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