Ellipse

An ellipse is the path traced out by a point that moves so that the sum of its distances from two fixed points, the foci of the ellipse, is constant. If the two foci coincide, the ellipse becomes a circle. If the sum of the distances equals the distance between the foci, the ellipse becomes the straight line joining these points.

The diameter through the two foci is called the major axis, and its length equals the sum of its distances from the foci. Half the length of the major axis is called the semi-major axis. The diameter that is the perpendicular bisector of the major axis is called the minor axis. Half the length of the minor axis is called the semi-minor axis. These axes are the longet and shortest diameters.

1 minus the rtio of the minor to the major axis is called the ellipticity of the ellipse. It ranges from 0 for a circle to 1 for a straight mline.

The area of an ellipse equals the product of pi, the semi-major axis and the semi-minor axis. There is no simple formula for the circumference (except in the case of a circle or a straight line); its calculation requires elliptic functions.

If a mirror is made in the shape of an ellipse, a beam of light passing through one focus will, after reflection, pass through the other focus. Continuing on, it will after successive reflections pass through each focus alternately, while getting closer and closer to the major axis.

An ellipse is one type of conic section.

According to Kepler's Laws, the orbit of a planet is an ellipse.