Introduction to the Ellipse

An ellipse is the set of all points, the sum of whose distances from two fixed points is a given positive constant that is greater than the distance between the fixed points. The two fixed points are called the foci (plural of focus). The midpoint of the line segment joining the foci is called the center of the ellipse. As shown in the given diagram $$F$$ and $$F’$$ are the foci of the ellipse, and $$O$$ is the center of the ellipse.

Major Axis: The line segment through the foci and across the ellipse is called the major axis of the ellipse. In the given diagram $$AA’$$ is the major axis of the ellipse.

Minor Axis: The line segment across the ellipse through the center and perpendicular to the major axis is called the minor axis of the ellipse. In the given diagram $$BB’$$ is the minor axis of the ellipse.

Vertices: The endpoints of the major axis are called the vertices of the ellipse. In the given diagram $$A$$ and $$A’$$ are the vertices of the ellipse.

Co-Vertices: The endpoints of the minor axis are called the co-vertices of the ellipse. In the given diagram $$B$$ and $$B’$$ are the co-vertices of the ellipse.

It is noted that the ellipse meets its major axis at the vertices. In the given diagram the foci of the ellipse are $$F$$ and $$F’$$, the vertices are $$A$$ and $$A’$$ its center is $$O$$.

Alternative Definition of Ellipse:
The ellipse can also be defined as the locus of a point in a plane whose distance from the fixed point bears a constant ratio to its distance from a fixed line. The fixed point is called the focus the fixed line is called the directrix, and the constant ratio is called the eccentricity. The eccentricity of the ellipse is denoted by $$e$$ and it is always greater than zero and less than one. The ellipse has two foci and two directrices.