Source : Webster's Revised Unabridged Dictionary (1913)

Asymptote \As"ymp*tote\ (?; 215), n. [Gr. ? not falling
   together; 'a priv. + ? to fall together; ? with + ? to fall.
   Cf. {Symptom}.] (Math.)
   A line which approaches nearer to some curve than assignable
   distance, but, though infinitely extended, would never meet
   it. Asymptotes may be straight lines or curves. A rectilinear
   asymptote may be conceived as a tangent to the curve at an
   infinite distance.

Source : WordNet®

asymptote
     n : a straight line that is the limiting value of a curve; can
         be considered as tangent at infinity; "the asymptote of
         the curve"