# Definition:Asymptote

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## Definition

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

## 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.