Circle

Definition :- A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.

The fixed point is called the centre of the circle and the distance from the centre to a point on the circle is called the radius of the circle

The equation of the circle is simplest if the centre of the circle is at the origin.

However, we derive below the equation of the circle with a given centre and radius
(Fig 11.12).
Given C (h, k) be the centre and r the radius of circle. Let P(x, y) be any point on

the circle (Fig11.12). Then, by the definition, | CP | = r . By the distance formula,

we have


This is the required equation of the circle with centre at (h,k) and radius r .