# Definition:Asymptote

## Definition

Asymptotes to $y = x + \dfrac 1 x$ (blue): $y$-axis, 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) $C$.

## Linguistic Note

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

It was coined by Apollonius of Perga during his analysis of conic sections.