Consider the equation of circle in general form is
Where are any constant values.
Rearrange the terms of the above equation (i) of 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 circle with standard equation of circle 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 circle.
Example: Find the centre and radius of the circle with the given equation of circle
Solution: We have given equation of circle is
We observe that in this equation of circle the coefficients of and is 7, but in the general form of equation of circle coefficients must be equal to 1.
To convert the given equation in form of general equation, dividing given equation both sides by 7, we get
The above equation cam be written as
Compare this equation with the general equation of circle as
We have the values , and .
Hence the centre of the circle is
Radius of the circle is