Definitions

from The American Heritage® Dictionary of the English Language, 4th Edition

  • n. 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.

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. A conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone.

from the GNU version of the Collaborative International Dictionary of English

  • n. A curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. It is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. See focus. If the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. Both curves are regarded as branches of the same hyperbola. See Illust. of Conic section, and focus.

from The Century Dictionary and Cyclopedia

  • n. A curve formed by the intersection of a plane with a double cone—that is, with two similar cones placed vertex to vertex, so that one is the continuation of the other.
  • n. An algebraic curve having asymptotes greater in number by one than its order. This meaning was introduced by Newton.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

  • n. an open curve formed by a plane that cuts the base of a right circular cone

Etymologies

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.
(American Heritage® Dictionary of the English Language, Fourth Edition)
From Ancient Greek ὑπερβολή (huperbolē). (Wiktionary)

Examples

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