hyperbola

[ hahy-pur-buh-luh ]

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 2 − y 2 /b 2 = ±1.

hyperbola

/ haɪˈpɜːbələ /

noun

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: 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

hyperbola

/ hī-pûr′bə-lə /

, Plural hyperbolas hī-pûr′bə-lē

1. 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.

hyperbola

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

Notes

The path of a comet that enters the solar system and then leaves forever is a hyperbolic curve (half of a hyperbola).

Word History and Origins

Origin of hyperbola¹

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

Word History and Origins

Origin of hyperbola¹

C17: from Greek huperbolē, literally: excess, extravagance, from hyper- + ballein to throw

Example Sentences

"Not every hyperbola is a burial or a grave — there's tree roots, there's masses, and other things in the substrate," Small says.

From Salon

Take a cone and cut it up; you get circles, ellipses, parabolas, and hyperbolas, depending on how you slice it.

From Literature

But most of the world of commodities is defined by hyperbola- or parabola-shaped curves.

From US News

“You can make a complete set of all four sconic sections: circle, ellipse, parabola and hyperbola,” the site explains, in step-by-step instructions that could easily swallow your entire weekend.

From New York Times

One of the portions of a curve that extends outwards to an indefinitely great distance; as, the branches of an hyperbola.

From Project Gutenberg

Related Words

• arc
• arch
• contour
• loop
• trajectory