Category:Latus Rectum

This category contains results about Latus Rectum.
Definitions specific to this category can be found in Definitions/Latus Rectum.

Definition

Definition 1

A latus rectum of a conic section $K$ is a chord of $K$ passing through a focus of $K$ perpendicular to the major axis of $K$.

Definition 2

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 $K$ perpendicular to the major axis of $K$.

Latus Rectum of Parabola

A parabola has only one focus, and does not have a minor axis, so the major axis is referred to just as the axis, hence the revised definition:

The latus rectum of a parabola $P$ is the chord of $P$ passing through the focus of $P$ perpendicular to the axis of $P$.

Latus Rectum of Hyperbola

A latus rectum of a hyperbola $K$ is a chord of $K$ passing through a focus of $K$ perpendicular to the major axis of $K$.

Also defined as

Some sources define the latus rectum with respect to the parabola only.

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

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