The point lies outside, on or inside the circle according as , and respectively.

The given equation of circle is

The centre of the circle (i) is and its radius is

In the given diagram, three different positions of the point are shown. It is clear from the diagram that if the point lies outside the circle, then its distance from the centre must be greater than its radius, i.e. . Similarly, the point lies on the circle, then its distance from the centre must be equal to the radius of circle i.e. and lies inside the circle, then its distance from the centre must be less than its radius i.e. . Combining these three situations, we note that the point lies outside, on or inside the circle according as

Now

Using the values of and from (ii) from (iv) in (iii), we have

__NOTE__**:** In fact, above formula status that to check the position of a point relative to a circle, we put the coordinates of the point in the equation of the circle

**(i)** if the result is positive, then the point lies outside the circle,

**(ii)** if the result is zero, then the point lies on the circle,

**(iii)** if the result is negative, then the point lies inside the circle.