How is the distance formula related to the equation of a circle?

is the required equation of a circle .

Step-by-step explanation:

We know that distance formula is the distance between any two points is given by:

⇒

⇒

Now, In equation of circle , Suppose we have center at  and arbitrary point in the circle is  . Distance between any point at circle to it's center is radius of circle i.e. r  , putting these values in distance formula we get:

⇒

⇒

⇒ , which the required equation of a circle .