The Collaborative International Dictionary of English v.0.48:

Parabola \Pa*rab"o*la\, n.; pl. Parabolas. [NL., fr. Gr. ?; --
   so called because its axis is parallel to the side of the
   cone. See Parable, and cf. Parabole.] (Geom.)
   (a) A kind of curve; one of the conic sections formed by the
       intersection of the surface of a cone with a plane
       parallel to one of its sides. It is a curve, any point of
       which is equally distant from a fixed point, called the
       focus, and a fixed straight line, called the directrix.
       See Focus.
   (b) One of a group of curves defined by the equation y =
       ax^n where n is a positive whole number or a positive
       fraction. For the cubical parabola n = 3; for the
       semicubical parabola n = 3/2. See under Cubical, and
       Semicubical. The parabolas have infinite branches, but
       no rectilineal asymptotes.
       [1913 Webster]

WordNet (r) 3.0 (2006):

parabola
    n 1: a plane curve formed by the intersection of a right
         circular cone and a plane parallel to an element of the
         curve

Moby Thesaurus II by Grady Ward, 1.0:

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