- 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.

Meaning of 'asymptote' (Princeton's WordNet)

1 . asymptote
[ n]

Meaning (1): - a straight line that is the limiting value of a curve; can be considered as tangent at infinity