hyperbola

American  

[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 2 − y 2 /b 2 = ±1.

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hyperbola British  

/ 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

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hyperbola Scientific  

/ hī-pûr′bə-lə /

plural

hyperbolas

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.

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hyperbola Cultural  

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

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Discover More

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

Etymology

Origin of hyperbola

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

Compare meaning

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

• ellipse vs. hyperbola

Explanation

Mathematically speaking, a hyperbola is an open plane curve. Like a parabola and an ellipse, a hyperbola is a kind of conic section, which is formed when a flat plane intersects a double cone. A hyperbola is a smooth plane curve, the curved line formed when a plane (a flat surface with no thickness) cuts through a double cone's base. When a spacecraft alters its course, using the Earth's gravity to propel it out into space, its orbit forms a hyperbola. This word is easy to confuse with hyperbole, or "exaggeration," and the two actually share a Greek root, also hyperbole, "extravagance" or "a throwing beyond."

Example Sentences

The foci must lie on the transverse axis and be in the interior of the hyperbola.

From Textbooks • Dec. 21, 2021

The a, b values in the equation also help us find the asymptotes of the hyperbola.

From Textbooks • May 6, 2020

In your own words, define a hyperbola and write the equation of a hyperbola centered at the origin in standard form.

From Textbooks • May 6, 2020

The rectangle and asymptotes are not part of the hyperbola, but they help us graph the hyperbola.

From Textbooks • May 6, 2020

In the hyperbola on the other hand d1 − d2 is constant, equal to the distance between the directrices, therefore in this case r1 − r2 is constant.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" by Various

Related Words

• arc
• arch
• contour
• loop
• trajectory