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 
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).
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chords