# Definition of a Circle

To understand the circle, consider the two dimensions $XY$-Plane. The set of all points in a plane which are equidistant from a fixed point in the plane is called a circle. The fixed point is called the centre of the circle. The fixed distance from the centre to the points of the circle is called the radius of the circle. If we draw a curve, keeping in mind the definition of circle, the curve in the diagram will be drawn. This is a circle here the centre is represented by $\left( {h,k} \right)$ and the radius is denoted by $r$.

If $C\left( {h,k} \right)$ and $r$ are the centre and the radius of the circle, respectively, then the set of the form $S\left( {C;r} \right) = \left\{ {P\left( {x,y} \right):\left| {CP} \right| = r} \right\}$ is a circle where $P\left( {x,y} \right)$ is any point of the circle. By this notation $\left| {CP} \right| = r$ it represents that the distance between point $P\left( {x,y} \right)$ and the centre $C\left( {h,k} \right)$ is equal to the radius.