The equation of a circle can be found using the centre and radius. The discriminant can determine the nature of intersections between two circles or a circle and a line to prove for tangency.

The general equation of a circle normally appears in the form

where is the centre of the circle

and is the radius.

Notice that for the circle to exist, .

Look at the following worked examples.

For

So the equation represents a circle with centre and radius

For

So does not represent a circle.

For we must write this starting with :

So the equation represents a circle with centre and radius

For each of the following equations, state whether it could represent a circle and if so, state the radius and centre.

- Question
So the equation represents a circle with centre and radius

- Question
So the equation does not represent a circle.