Definition:Asymptote

Definition

 * Asymptote.png, and the line $x = y$ (red)]]

Let $C$ be a curve in the plane.

Let $L$ be a straight (infinite) line such that the distance between $C$ and $L$ approaches zero as they tend to infinity.

Then $L$ is an asymptote to (or of) $C$.

Also see

 * Definition:Horizontal Asymptote
 * Definition:Vertical Asymptote


 * Definition:Asymptote of Hyperbola

Linguistic Note
The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos) which means not falling together.

It was coined by during his analysis of conic sections.