Hyperbola

:For hyperbole, the figure of speech, see hyperbole.

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In mathematics, a hyperbola is a type of conic section (literally: 'exaggeration' from the Greek {{polytonic|????????}}) defined as the intersection between a cone and a plane which cuts through both halves of the cone.

Related Topics:
Mathematics - Conic section - Greek - Cone - Plane

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It may also be defined as the set of all points for which the difference in the distance to two fixed points (called the foci) is constant.

Related Topics:
Set - Points - Distance - Foci

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For a simple geometric proof that the two characterizations above are equivalent to each other, see Dandelin spheres.

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Algebraically, a hyperbola is a curve in the Cartesian plane defined by

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an equation of the form

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:A x^2 + B xy + C y^2 + D x + E y + F = 0

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such that B^2 > 4 AC, where all of the coefficients are real, and where more that one solution, defining a pair of points (x, y) on the hyperbola, exists.

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