In mathematics, an ellipse is a curve around two focal points on a plane, so for each point on the curve, the sum of the distances to the two focal points is constant. Therefore, it is a generalization of a circle, and it is a special type of ellipse with two focuses at the same position. The shape of an ellipse is represented by its eccentricity, which can be any number from 0 to close to but less than 1.

An ellipse is a closed cone section: a plane curve intersects a plane through a cone. There are many similarities between the other two forms of ellipse and cone section: parabola and hyperbola, which are both open and unbounded. The cross section of a cylinder is elliptical unless it is perpendicular to the axis of the cylinder.

An ellipse can also be defined as a set of points, so that the ratio of the distance between each point on the curve and a given point (called focus) to the distance between the same point on the curve (called directrix) is a constant. This ratio is called eccentricity of ellipse.

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Definition:

The locus of the moving point P whose sum of the distances between two fixed points on a plane is equal to a constant is called an ellipse.

Namely:

These two fixed points are called the focal points of the ellipse, and the distance between the two focal points is called the focal length of the ellipse. Is the moving point of an ellipse.

The chord obtained by cutting the ellipse into a line coincident with the line connecting the two focal points is the long axis and the length is a.

The ellipse cuts a straight line, which bisects the straight line connecting the two focal points vertically. The chord is the short axis and the length is b..