# hyperbola

[hahy-pur-buh-luh]

- 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 2 − y 2/b 2 = ±1.

## Origin of hyperbola^{}

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## 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.

Carpentry for BoysJ. S. Zerbe

#### I said, "if my orbit is a hyperbola, I shall never return to earth."

Christmas Eve and Christmas DayEdward 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.

Fables of Infidelity and Facts of FaithRobert Patterson

# hyperbola

- 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: x ²/ a ² – y ²/ b ² = 1 where 2 a is the distance between the two intersections with the x -axis and b = a √(e ² – 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
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## 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

# hyperbola

[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® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

# hyperbola

[(heye-pur-buh-luh)]

## 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
Copyright © 2005 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.