# hyperbola

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## hy·per·bo·la

(hī-pûr′bə-lə)*n.*

*pl.*

**hy·per·bo·las**or

**hy·per·bo·lae**(-lē)

A plane curve having two branches, formed by the intersection of a plane with both halves of a right circular cone at an angle parallel to the axis of the cone. It is the locus of points for which the difference of the distances from two given points is a constant.

[New Latin, from Greek huperbolē,

*a throwing beyond, excess (from the relationship between the line joining the vertices of a conic and the line through its focus and parallel to its directrix)*; see**hyperbole**.]## hyperbola

(haɪˈpɜːbələ)*n*,

*pl*

**-las**

*or*

**-le**(-ˌliː)

(Mathematics) 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[C17: from Greek

*huperbolē,*literally: excess, extravagance, from hyper- +*ballein*to throw]## hy•per•bo•la

art at hyperfunction

(haɪˈpɜr bə lə) *n.,*

*pl.*

**-las.**

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 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. See also diag. at conic section.[1660–70; < New Latin < Greek

*hyperbolḗ*literally, excess]## hy·per·bo·la

(hī-pûr′bə-lə) 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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Noun | 1. | hyperbola - an open curve formed by a plane that cuts the base of a right circular coneconic, conic section - (geometry) a curve generated by the intersection of a plane and a circular cone |

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