# hyperbola

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## hyperbola

a plane curve having two branches
Not to be confused with:
hyperbole – an exaggeration used as a figure of speech: That dog’s so ugly its face could stop a clock.
Abused, Confused, & Misused Words by Mary Embree Copyright © 2007, 2013 by Mary Embree
hyperbola
The equation of this hyperbola is
x2 - y2 = 1.

## hy·per·bo·la

(hī-pûr′bə-lə)
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.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## hyperbola

(haɪˈpɜːbələ)
n, pl -las or -le (-ˌliː)
(Mathematics) 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/a2y2/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]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## hy•per•bo•la

art at hyperfunction
(haɪˈpɜr bə lə)

n., pl. -las.
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 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. See also diag. at conic section.
[1660–70; < New Latin < Greek hyperbolḗ literally, excess]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
hyperbola

## hy·per·bo·la

(hī-pûr′bə-lə)
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.
The American Heritage® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 hyperbola - an open curve formed by a plane that cuts the base of a right circular coneconic, conic section - (geometry) a curve generated by the intersection of a plane and a circular cone
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
хипербола
hyperbola
hyperbeli
hiperbola
hyperbel

## hyperbola

[haɪˈpɜːbələ] N (hyperbolas or hyperbole (pl)) [haɪˈpɜːbəliː]
Collins Spanish Dictionary - Complete and Unabridged 8th Edition 2005 © William Collins Sons & Co. Ltd. 1971, 1988 © HarperCollins Publishers 1992, 1993, 1996, 1997, 2000, 2003, 2005

## hyperbola

n (Math) → Hyperbel f
Collins German Dictionary – Complete and Unabridged 7th Edition 2005. © William Collins Sons & Co. Ltd. 1980 © HarperCollins Publishers 1991, 1997, 1999, 2004, 2005, 2007
References in classic literature ?
"Yes," said Nicholl, "it will follow either a parabola or a hyperbola."
"With a certain speed it will assume the parabola, and with a greater the hyperbola."
"The hyperbola, Michel, is a curve of the second order, produced by the intersection of a conic surface and a plane parallel to its axis, and constitutes two branches separated one from the other, both tending indefinitely in the two directions."
"What I particularly like in your definition of the hyperbola (I was going to say hyperblague) is that it is still more obscure than the word you pretend to define."
One maintained the hyperbola, the other the parabola.
"Now, gentlemen cosines, will you cease to throw parabolas and hyperbolas at each other's heads?
Its four-stage Hyperbola 1 rocket achieved lift off from the Jiuquan space base, located in China's Inner Mongolia autonomous region, and carried several small satellites and other payloads into an orbit approximately 300 kilometres above Earth, according to the company.
This problem made Khayyam to succeed in solving the cubic equation x3 + 200x = 20x2 + 2000 and he found a positive root of this cubic by considering the intersection of a rectangular hyperbola and a circle.
The area under the hyperbola y = 1/x between x = 1 and x = w, for example, turns out to be complicated, but its properties enable it to be used to define natural logarithms in a rigorous way.
If you still remember what a hyperbola looks like, that's the shape that forms when you plot the number of people who are willing to wait longer for the better reward against the waiting time.
This is an equilateral hyperbola, for which the coordinate axes are the asymptotes (Fig.

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