# Standard Equation of a Circle

Let be any point of the circle as shown in the diagram, then by the definition of circle, the distance of point from must be equal to the radius of the circle . i.e. .

As we know that distance formula from the analytic geometry as

Now we shall use this formula to establish the equation of circle, consider the points and , now using distance formula for these two points as:

Squaring both sides, we have

This is the equation of circle with centre and radius . This is called the equation of circle in standard form.

__Note__**:** If the centre of the circle is at origin , then , so the equation of circle takes the form

This is the equation of the circle with radius and the centre at the origin in two dimensions

*XY-*plane.

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

__Solution__**:** Form the given data of the example we have centre and radius . In this situation we use the standard form of equation of circle is

By the given condition and , so putting these values in the given equation of circle, we have

This is the required equation of the circle.