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 
measured from a focus
such that
 |
(1) |
where 
and 
are the apoapsis and periapsis,
and 
is the ellipse's eccentricity.
Plugging in for 
and 
then gives
 |
(2) |
so
 |
(3) |
For a parabola,
 |
(4) |
where 
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.
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Cite this as:
Weisstein, Eric W. "Semilatus Rectum." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SemilatusRectum.html