# General Form of the Equation of a Circle

Consider the equation of a circle in general form is

Where are any constant values.

If we rearrange the terms of the above equation (i) of a circle, we have

In this equation we use the method of completing squares, so for this we need to add and on both sides of the equation (ii). i.e.:

Compare this equation of a circle with the standard equation of a circle and we get the radius and centre .

This shows that the equation represents a circle with centre and radius . This is called the general equation of a circle.

__Example__**:** Find the centre and radius of the circle with the given equation of a circle

__Solution__**:** The given equation of a circle is

We observe that in this equation of a circle the coefficients of and is **7**, but in the general form of the equation of a circle the coefficients must be equal to **1**.

To convert the given equation into the form of general equation, divide the given equation on both sides by **7.** We get

The above equation can be written as

Compare this equation with the general equation of a circle as

We have the values , and .

Hence the centre of the circle is

The radius of the circle is