# How do you find the equation of a circle?

###### Wiki User

###### 2009-02-01 21:57:41

A circle is the locus of all points equidistant from a fixed

point on the plane. The fixed point is called the centre of the

circle and the equal distance is called the radius of the

circle.

We can derive the equation of the circle from the distance

formula.

Let O be the centre of the circle and r be the radius of the

circle.

Here the centre = Origin = (0, 0) and the radius = r units.

The distance r = sqrt ((x-0)2 + (y-0)2)

r = sqrt (x2 + y2)

Squaring both the sides, we get x2 + y2 = r2

This is the equation of the circle with centre as Origin.

If the centre point is some (h, k), then use the distance

formula to find the radius r.

The distance r = sqrt ((x-h)2 + (y-k)2)

Squaring both sides, we get (x-h)2 + (y-k)2 = r2.

This is the equation of the circle with centre as the point (h,

k).