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# hyperbola

[ hahy-**pur**-b*uh*-l*uh* ]

## 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.

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## Notes

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## Word History and Origins

Origin of hyperbola^{1}

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## Word History and Origins

Origin of hyperbola^{1}

*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:

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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.

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

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

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

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

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

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