Definition:Conic Section/Eccentricity

From ProofWiki
Jump to navigation Jump to search

This page is about Eccentricity of Conic Section. For other uses, see eccentricity.


Let $K$ be a conic section specified in terms of:

a given straight line $D$
a given point $F$
a given constant $e$

where $K$ is the locus of points $P$ such that the distance $p$ from $P$ to $D$ and the distance $q$ from $P$ to $F$ are related by the condition:

$q = e p$

The constant $e$ is known as the eccentricity of the conic section.

Also denoted as

Some sources use $\epsilon$ for the eccentricity of a conic section.

Also see

  • Results about the eccentricity of a conic section can be found here.

Historical Note

The focus-directrix definition of a conic section was first documented by Pappus of Alexandria.

It appears in his Collection.

As he was scrupulous in documenting his sources, and he gives none for this construction, it can be supposed that it originated with him.