View synonyms for hyperbola

hyperbola

[ hahy-pur-buh-luh ]

Phonetic (Standard)IPA

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 2 − y 2 /b 2 = ±1.

hyperbola

/ haɪˈpɜːbələ /

noun

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

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

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

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Notes

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

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Word History and Origins

Origin of hyperbola¹

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

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Word History and Origins

Origin of hyperbola¹

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

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Compare Meanings

How does hyperbola compare to similar and commonly confused words? Explore the most common comparisons:

ellipse vs. hyperbola

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Example Sentences

What’s more, the two given points were the local maximum and minimum of the two halves of the hyperbola.

From FiveThirtyEight

The planet would then have moved in a parabola, or an hyperbola, curves not returning into themselves.

From Project Gutenberg

To assimilate the hyperbola to the ellipse was rather to contradict this evidence.

From Project Gutenberg

Only on the assumption that the social value curve for this totality of commodities is a rectangular hyperbola.

From Project Gutenberg

When the conic is a hyperbola the meridian line is in the form of a looped curve (fig. 12).

From Project Gutenberg

This is the equation of an hyperbola whose center is on the axis of abscisses.

From Project Gutenberg

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