The Lesson
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.
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
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^{2} − y^{2} + x + 2y − 3 = 0
...it isn't an equation of a circle.