# Standard Equation of a Circle

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

As we know the distance formula from the analytic geometry as

Now we shall use this formula to establish the equation of the circle. Consider the points and . Now using the distance formula for these two points as

Squaring both sides, we have

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

__Note__**:** If the centre of the circle is at origin , then , so the equation of the 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__**:** From the given data in the example we have centre and radius . In this situation we use the standard form of equation of a circle, which is:

Given the condition and , putting these values in the given equation of a circle, we have

This is the required equation of the circle.