Definition:Latus Rectum/Definition 2

Definition

A latus rectum of a conic section $K$ is a chord of $K$ passing through a focus of $K$ parallel to the directrix of $K$.

Examples

Latus Rectum of Circle

The circle, being a degenerate ellipse whose foci coincide, properly has no latus rectum, as a circle has neither a directrix nor a major axis.

However, there is a case to make that, in a sense, a diameter of a circle $C$ can be considered as a latus rectum of $C$.

Latus Rectum of Ellipse

A latus rectum of an ellipse $K$ is a chord of $K$ passing through a focus of $K$ parallel to the directrix of $K$.

Latus Rectum of Parabola

A parabola has only one focus, hence the revised definition:

The latus rectum of a parabola $P$ is the chord of $P$ passing through the focus of $P$ parallel to the directrix $D$.

Latus Rectum of Hyperbola

A latus rectum of a hyperbola $K$ is a chord of $K$ passing through a focus of $K$ parallel to the directrix of $K$.

Also see

• Equivalence of Definitions of Latus Rectum

• Results about the latus rectum can be found here.

Linguistic Note

The term latus rectum is a compound of the Latin:

latus, meaning side

rectum, meaning straight or right, as in straight line or right angle.

Hence it literally means right side or straight side.

Its plural is latera recta.

Sources

Weisstein, Eric W. "Latus Rectum." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LatusRectum.html