as·ymp·tote (ăsĭm-tōt′, -ĭmp-)
A line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve.
[Ultimately from Greek asumptōtos, not intersecting : a-, not; see A-1 + sumptōtos, intersecting (from sumpiptein, sumptō-, to converge : sun-, syn- + piptein, to fall; see pet- in the Appendix of Indo-European roots).]
as′ymp·totic (-tŏtĭk), as′ymp·toti·cal adj.
(click for a larger image)asymptote
The x-axis and y-axis are asymptotes of the hyperbola xy = 3.
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