AsymptoteIn analytic geometry, an asymptote (ˈæsɪmptoʊt) of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity. The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos) which means "not falling together", from ἀ priv. + σύν "together" + πτωτ-ός "fallen".