The Collaborative International Dictionary of English v.0.48:

Hyperbola \Hy*per"bo*la\, n. [Gr. ?, prop., an overshooting,
   excess, i. e., of the angle which the cutting plane makes
   with the base. See Hyperbole.] (Geom.)
   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.
   [1913 Webster]

WordNet (r) 3.0 (2006):

hyperbola
    n 1: an open curve formed by a plane that cuts the base of a
         right circular cone

Moby Thesaurus II by Grady Ward, 1.0:

18 Moby Thesaurus words for "hyperbola":
   arc, bow, catacaustic, catenary, caustic, circle, conchoid, crook,
   curl, curve, diacaustic, ellipse, festoon, hook, lituus, parabola,
   sinus, tracery