Ellipse: Difference between revisions
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Revision as of 12:15, 18 February 2025
Ellipse is a term used in geometry to describe a specific type of curve on a plane. It is one of the four types of conic section, the others being the circle, parabola, and hyperbola. An ellipse can be defined as the locus of all points that the sum of the distances from two fixed points (the foci) is constant.
Definition
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same.
Properties
An ellipse has several unique properties. These include:
- The sum of the distances from any point on the ellipse to the two foci is constant.
- The ratio of the distance of a point on the ellipse from one focus to the distance from that point to the directrix is a constant, e, the eccentricity of the ellipse.
- The area of an ellipse is πab, where a and b are the semi-major and semi-minor axes, respectively.
Applications
Ellipses have many applications in various fields such as physics, engineering, and astronomy. For example, the orbits of planets around the sun are ellipses with the sun at one of the foci. In addition, the design of whispering galleries and certain types of acoustic 'sweet spots' also make use of the properties of ellipses.
