Equation of a circle is based on the definition of the circle: A circle is a set of points which are at equal distance from its center.

So the equation of the circle is derived using distance formula.

Let the center of a circle be at a point (h, k) and its radius be r,

Then distance of center from any point (x, y) lying on the circle is given by
$d^2$ = $\sqrt{(x - h)^2 + (y - k)^2}$

As distance between the center and the point on the center = radius = r

we get
r = $\sqrt{(x - h)^2 + (y - k)^2}$

$r^2$ = $(x - h)^2$ + $(y - k)^2$

Circle Equation

Equation of a circle can be written in the form

$x^2 + y^2 + Ax + By + C = 0$

The center – radius form of the equation of the circle is called as standard form of the equation.

$(x - h)^2 + (y - k)^2 = r^2$