A circle is a closed curve in the plane that is defined as the set of all points that are a given distance from a given point. The given distance, i.e., the distance from the center to any point on the circle, is called the radius. Any line connecting two points on the circle (i.e., a chord) that also passes through the center is called a diameter. The circumference of any circle is \(\pi\) times the diameter (equivalently, twice \(\pi\) times the radius). The area of a circle is \(\pi\) times the square of the radius. The familiar formulas are:

\[\begin{eqnarray*} C & = & \pi D = 2\pi r \\ & & \\ & & \\ A & = & \pi r^2 \end{eqnarray*}\]

Algebraically, a circle in the Cartesian plane is a relation defined by an equation of the form \((x-h)^2+(y-k)^2=r^2\), where the point \((h,k)\) is the center of the circle and \(r\) is the radius.

Figure 1: A circle in the Cartesian plane.

As a conic curve a circle is an ellipse of eccentricity 0.