Equation of a Circle (in General Form)
(KS3, Year 7)

The Lesson

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 anything 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 centre and radius:
x2 + y2 − 2x − 4x − 4 = 0 (x − 1)2 + (y − 2)2 = 9
This circle has centre (1, 2) and radius 3. Read more about converting an equation of a circle in general form to standard form

The Signs in the Equation

The equation of a circle in general form is:
x2 + y2 + Ax + By + C = 0
A, B and C can be positive or negative or even 0. For example,
  • A = 1, B = −2 and C = 3
  • A = −4, B = 0 and C = −5
However, the equations always starts x2 + y2 + .... If you see an equation such as...
x2 − y2 + x + 2y − 3 = 0
...it isn't an equation of a circle.
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See Also

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