# Ellipse

An ellipse is defined as the collection of points P on a plane, such that sum of its distances from two fixed points F

_{1}and F

_{2}is a constant. The fixed point F

_{1}and F

_{2}are called foci of the ellipse (see in figure given below.).

# Alternative Definition

An ellipse is defined as the collection of points P on a plane, such that its distance from a fixed point F

_{1}[F

_{2}] bears a constant ratio e(e<1) to its distance from a fixed line D

_{1}[D

_{2}]. The fixed point F

_{1}[F

_{2}] is called focus of the ellipse, D

_{1}[D

_{2}] is called its directrix and e is called as eccentricity of the ellipse (see in figure given below.).

_{1}and F

_{2}. The line containing the foci is called the major axis. The midpoint of the foci is called the centre of the ellipse. The line through the centre and perpendicular to the major axis is called the minor axis. The two points of intersection of the ellipse with major axis are called the vertices, V

_{1}and V

_{2}of the ellipse. The distance from one vertex to the other is called the length of the major axis. The ellipse is symmetric with respect to its major axis and with respect to its minor axis.