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

In this equation,

In this example,
This circle has centre
Please tell us using

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.

## 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:x^{2} + y^{2} − 2x − 4x − 4 = 0

(x − 1)^{2} + (y − 2)^{2} = 9

**(1, 2)**and radius**3**. 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:
x

^{2}+ y^{2}+ 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

**x**. If you see an equation such as...^{2}+ y^{2}+ ...
x

...it isn't an equation of a circle.
^{2}− y^{2}+ x + 2y − 3 = 0## You might also like...

graphs and coordinate geometryfinding the center and radius from the equation of a circleconverting an equation of a circle from general to standard formnumbers curriculum

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## Worksheet

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