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)
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where and are the apoapsis and periapsis, and is the ellipse's eccentricity. Plugging in for and then gives
(2)
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so
(3)
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For a parabola,
(4)
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where is the distance between the focus and vertex (or directrix).