The Collaborative International Dictionary of English v.0.48:

Parabolic \Par`a*bol"ic\, Parabolical \Par`a*bol"ic*al\, a. [Gr.
   paraboliko`s figurative: cf. F. parabolique. See Parable.]
   [1913 Webster]
   1. Of the nature of a parable; expressed by a parable or
      figure; allegorical; as, parabolical instruction.
      [1913 Webster]

   2. [From Parabola.] (Geom.)
      (a) Having the form or nature of a parabola; pertaining
          to, or resembling, a parabola; as, a parabolic curve.
      (b) Having a form like that generated by the revolution of
          a parabola, or by a line that moves on a parabola as a
          directing curve; as, a parabolic conoid; a parabolic
          reflector; a parabolic antenna.
          [1913 Webster +PJC]

   Parabolic conoid, a paraboloid; a conoid whose directing
      curve is a parabola. See Conoid.

   Parabolic mirror (Opt.), a mirror having a paraboloidal
      surface which gives for parallel rays (as those from very
      distant objects) images free from aberration. It is used
      in reflecting telescopes.

   Parabolic spindle, the solid generated by revolving the
      portion of a parabola cut off by a line drawn at right
      angles to the axis of the curve, about that line as an
      axis.

   Parabolic spiral, a spiral curve conceived to be formed by
      the periphery of a semiparabola when its axis is wrapped
      about a circle; also, any other spiral curve having an
      analogy to the parabola.
      [1913 Webster]

WordNet (r) 3.0 (2006):

parabolical
    adj 1: resembling or expressed by parables [syn: parabolic,
           parabolical]
    2: having the form of a parabola [syn: parabolic,
       parabolical]