Definition:Latus Rectum/Definition 1
Definition
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 $K$.
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 see
- 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
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): latus rectum (pl.latera recta)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): latus rectum
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): latus rectum