Ellipse

Overview

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Circles

A circle is a special kind of ellipse consisting of all points in a plane at a given distance from a given point, i.e. the center. In this way, a circle is characterized by its center and radius, the distance from the center to any point of the circle.

The perimeter of a circle is known as its circumference. A circle with radius $r$ has circumference $2\pi r$ and area $\pi r^2$. A continuous segment along the circumference of a circle is called an arc.

A chord through the center of the circle is a diameter. The two points $P$ and $Q$ at the end of a diameter are antipodal (or diametrically opposed). $P$ is an antipode of $Q$.

Disks

A disk is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary. Its said to be open otherwise.

Cartesian Equation

Within the Cartesian coordinate system, the equation of a circle with radius $r$ and center $⟨h,k⟩$ is