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

There are also four options when we consider a circle and a hyperbola.

From Textbooks • May 6, 2020

The two points where the transverse axis intersects the hyperbola are each a vertex of the hyperbola.

From Textbooks • May 6, 2020

We will see that the equation of a hyperbola looks the same as the equation of an ellipse, except it is a difference rather than a sum.

From Textbooks • May 6, 2020

The two axes of the ellipse are the major axis and the minor axis, and the two axes of the hyperbola are the transverse axis and the conjugate axis.

From Webster's Unabridged Dictionary (2nd 100 Pages) by Webster, Noah

Related Words

• arc
• arch
• contour
• loop
• trajectory