Semilatus Rectum

The chord through a focus parallel to the conic section directrix of a conic section is called the latus rectum, and half this length is called the semilatus rectum (Coxeter 1969). "Semilatus rectum" is a compound of the Latin semi-, meaning half, latus, meaning 'side,' and rectum, meaning 'straight.'

For an ellipse, the semilatus rectum is the distance L measured from a focus such that

where r_+=a(1+e) and r_-=a(1-e) are the apoapsis and periapsis, and e is the ellipse's eccentricity. Plugging in for r_+ and r_- then gives

so

For a parabola,

where a is the distance between the focus and vertex (or directrix).

See also

Apoapsis, Conic Section, Conic Section Directrix, Eccentricity, Ellipse, Focal Parameter, Focus, Latus Rectum, Periapsis, Semimajor Axis, Semiminor Axis, Universal Parabolic Constant

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References

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 116-118, 1969.

Referenced on Wolfram|Alpha

Semilatus Rectum

Cite this as:

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

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