**asymptote**

In 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.