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hyperbola

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hy⋅per⋅bo⋅la

[hahy-pur-buh-luh]
–noun Geometry.
the set of points in a plane whose distances to two fixed points in the plane have a constant difference; a curve consisting of two distinct and similar branches, formed by the intersection of a plane with a right circular cone when the plane makes a greater angle with the base than does the generator of the cone. Equation: x2/a2y2/b2 = ±1.


Origin:
1660–70; < NL < Gk hyperbol the geometrical term, lit., excess. See hyperbole
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
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hy·per·bo·la   (hī-pûr'bə-lə)   


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n.   pl. hy·per·bo·las or hy·per·bo·lae (-lē)
A plane curve having two branches, formed by the intersection of a plane with both halves of a right circular cone at an angle parallel to the axis of the cone. It is the locus of points for which the difference of the distances from two given points is a constant.

[New Latin, from Greek huperbolē, a throwing beyond, excess (from the relationship between the line joining the vertices of a conic and the line through its focus and parallel to its directrix); see hyperbole.]
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Cultural Dictionary

hyperbola [(heye-pur-buh-luh)]

In geometry, a curve having a single bend, with lines going infinitely far from the bend.

Note: The path of a comet that enters the solar system and then leaves forever is a hyperbolic curve (half of a hyperbola).
The American Heritage® New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Word Origin & History

hyperbola 
1668, from Gk. hyperbole "extravagance," lit. "a throwing beyond" (see hyperbole). Perhaps so called because the inclination of the plane to the base of the cone exceeds that of the side of the cone.
Online Etymology Dictionary, © 2001 Douglas Harper
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