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What (who) is conic sections - definition
![The parabola is a member of the family of [[conic section]]s.](https://commons.wikimedia.org/wiki/Special:FilePath/Conic Sections.svg?width=200 "The parabola is a member of the family of [[conic section]]s.")
![Parabolic compass designed by [[Leonardo da Vinci]]](https://commons.wikimedia.org/wiki/Special:FilePath/Leonardo parabolic compass.JPG?width=200 "Parabolic compass designed by [[Leonardo da Vinci]]")
![A [[bouncing ball]] captured with a stroboscopic flash at 25 images per second. The ball becomes significantly non-spherical after each bounce, especially after the first. That, along with spin and [[air resistance]], causes the curve swept out to deviate slightly from the expected perfect parabola.](https://commons.wikimedia.org/wiki/Special:FilePath/Bouncing ball strobe edit.jpg?width=200 "A [[bouncing ball]] captured with a stroboscopic flash at 25 images per second. The ball becomes significantly non-spherical after each bounce, especially after the first. That, along with spin and [[air resistance]], causes the curve swept out to deviate slightly from the expected perfect parabola.")
![The path (in red) of [[Comet Kohoutek]] as it passed through the inner Solar system, showing its nearly parabolic shape. The blue orbit is the Earth's.](https://commons.wikimedia.org/wiki/Special:FilePath/Comet Kohoutek orbit p391.svg?width=200 "The path (in red) of [[Comet Kohoutek]] as it passed through the inner Solar system, showing its nearly parabolic shape. The blue orbit is the Earth's.")
![The supporting cables of [[suspension bridge]]s follow a curve that is intermediate between a parabola and a [[catenary]].](https://commons.wikimedia.org/wiki/Special:FilePath/Laxmanjhula.jpg?width=200 "The supporting cables of [[suspension bridge]]s follow a curve that is intermediate between a parabola and a [[catenary]].")
![Rainbow Bridge]] across the [[Niagara River]], connecting [[Canada]] (left) to the [[United States]] (right). The parabolic arch is in compression and carries the weight of the road.](https://commons.wikimedia.org/wiki/Special:FilePath/Rainbow Bridge(2).jpg?width=200 "Rainbow Bridge]] across the [[Niagara River]], connecting [[Canada]] (left) to the [[United States]] (right). The parabolic arch is in compression and carries the weight of the road.")
![Parabolic shape formed by a liquid surface under rotation. Two liquids of different densities completely fill a narrow space between two sheets of transparent plastic. The gap between the sheets is closed at the bottom, sides and top. The whole assembly is rotating around a vertical axis passing through the centre. (See [[Rotating furnace]])](https://commons.wikimedia.org/wiki/Special:FilePath/Parabola shape in rotating layers of fluid.jpg?width=200 "Parabolic shape formed by a liquid surface under rotation. Two liquids of different densities completely fill a narrow space between two sheets of transparent plastic. The gap between the sheets is closed at the bottom, sides and top. The whole assembly is rotating around a vertical axis passing through the centre. (See [[Rotating furnace]])")
![[[Solar cooker]] with [[parabolic reflector]]](https://commons.wikimedia.org/wiki/Special:FilePath/ALSOL.jpg?width=200 "[[Solar cooker]] with [[parabolic reflector]]")
![[[Parabolic antenna]]](https://commons.wikimedia.org/wiki/Special:FilePath/Antenna 03.JPG?width=200 "[[Parabolic antenna]]")
![[[Parabolic microphone]] with optically transparent plastic reflector used at an American college football game.](https://commons.wikimedia.org/wiki/Special:FilePath/ParabolicMicrophone.jpg?width=200 "[[Parabolic microphone]] with optically transparent plastic reflector used at an American college football game.")
![Array of [[parabolic trough]]s to collect [[solar energy]]](https://commons.wikimedia.org/wiki/Special:FilePath/Solar Array.jpg?width=200 "Array of [[parabolic trough]]s to collect [[solar energy]]")
![Edison]]'s searchlight, mounted on a cart. The light had a parabolic reflector.](https://commons.wikimedia.org/wiki/Special:FilePath/Ed d21m.jpg?width=200 "Edison]]'s searchlight, mounted on a cart. The light had a parabolic reflector.")
![Physicist [[Stephen Hawking]] in an aircraft flying a parabolic trajectory to simulate zero gravity](https://commons.wikimedia.org/wiki/Special:FilePath/Physicist Stephen Hawking in Zero Gravity NASA.jpg?width=200 "Physicist [[Stephen Hawking]] in an aircraft flying a parabolic trajectory to simulate zero gravity")
Wikipedia
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface.
The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola that is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola—that is, all parabolas are geometrically similar.
Parabolas have the property that, if they are made of material that reflects light, then light that travels parallel to the axis of symmetry of a parabola and strikes its concave side is reflected to its focus, regardless of where on the parabola the reflection occurs. Conversely, light that originates from a point source at the focus is reflected into a parallel ("collimated") beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with sound and other waves. This reflective property is the basis of many practical uses of parabolas.
The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design of ballistic missiles. It is frequently used in physics, engineering, and many other areas.
