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# hyperbola

[hahy-pur-buh-luh] /haɪˈpɜr bə lə/
noun, Geometry.
1.
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.
Origin of hyperbola
1660-1670
1660-70; < New Latin < Greek hyperbolḗ the geometrical term, literally, excess. See hyperbole
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2018.
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Examples from the Web for hyperbola
Historical Examples
• An oval is never mistaken for a circle, nor an hyperbola for an ellipsis.

• If the cone is cut off vertically on the dotted line, A, the curve is a hyperbola.

J. S. Zerbe
• I said, "if my orbit is a hyperbola, I shall never return to earth."

Edward E. Hale
• The curve is in this case called an hyperbola (see fig. 20).

• In the hyperbola we have the mathematical demonstration of the error of an axiom.

Robert Patterson
• Two of the sides of the triangle in this proposition constitute a special form of the hyperbola.

David Eugene Smith
• If the plane tips the slightest amount more, the section becomes an hyperbola.

David Eugene Smith
• The axes of an hyperbola bisect the angles between the asymptotes.

• Similarly, in an hyperbola a vertex is nearer 704 to the directrix than to the focus.

• With a certain speed it will assume the parabola, and with a greater the hyperbola.

British Dictionary definitions for hyperbola

## hyperbola

/haɪˈpɜːbələ/
noun (pl) -las, -le (-ˌliː)
1.
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
Word Origin
C17: from Greek huperbolē, literally: excess, extravagance, from hyper- + ballein to throw
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Word Origin and History for hyperbola
n.

1660s, from Latinized form of Greek hyperbole "extravagance," literally "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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hyperbola in Science
 hyperbola   (hī-pûr'bə-lə)    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.
The American Heritage® Science Dictionary
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hyperbola in Culture
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 New Dictionary of Cultural Literacy, Third Edition
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### Difficulty index for hyperbola

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### Word Value for hyperbola

0
20
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