The set of all points in the Cartesian plane that are equal distance from a fixed point is called a circle. The fixedpoint is called the center of the circle, and the distance from the center of the circle to any point on the circle is called the radius of the circle.

If C(h, k) is the center of a circle, r its radius and p(x, y) any point on the circle is denoted by notation

Center of circle notation

By distance formula we get

is an equation of the circle in standard form on the Cartesian plane.

Center of circle at origin

if the center of circle at origin, then equation of circle in standard form become.

Point circle

if r =0, the circle is called point circle.

Which consist of the circle only.

Parametric equation of circle

Let P(x, y) any point in the center of circle at origin

And let inclination of OP be θ (theta) in diagram

it is clear that

x= r cos θ

y= r sin θ

The point P (r cos θ, r sin θ) for all values of a theta (θ) are called parametric

equation of circle.

General form of an equation of circle on the Cartesian plane.

The equation

represent a circle g, f, and c being constant.

This equation can be written in the form

after simplification

which is the standard form of an equation of a circle with center (-g, -f)

and radius

Thus, equation A is called the standard form of an equation of circle.