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: x 2 /a 2y 2 /b 2 = ±1.

1660–70; < Neo-Latin < Greek hyperbolḗ the geometrical term, literally, excess. See hyperbole

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World English Dictionary
hyperbola (haɪˈpɜːbələ)
n , pl -las, -le
a conic section formed by a plane that cuts both bases of a cone; it consists of two branches asymptotic to two intersecting fixed lines and has two foci. Standard equation: x²/a² -- y²/b² = 1 where 2a is the distance between the two intersections with the x-axis and b = a√(e² -- 1), where e is the eccentricity
[C17: from Greek huperbolē, literally: excess, extravagance, from hyper- + ballein to throw]

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Word Origin & History

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, © 2010 Douglas Harper
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American Heritage
Science Dictionary
hyperbola   (hī-pûr'bə-lə)  Pronunciation Key 

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Plural hyperbolas or hyperbolae (hī-pûr'bə-lē)
A plane curve having two separate parts or branches, formed when two cones that point toward one another are intersected by a plane that is parallel to the axes of the cones.
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Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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American Heritage
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
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Published by Houghton Mifflin Company. All rights reserved.
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