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Latus Rectum of Hyperbola

It is a chord of the hyperbola which passes through one of the foci and is perpendicular to the transverse axis.
If LL' is one the latus rectum, then (ae, F2L) lies on the hyperbola (1)
Since L lies on (1)

⇒ F2L2 = b2 (e2 - 1) = b2                              [a2(e2-1) = b2]
F2L = .
Thus, length of the latus rectum LL' is 2.

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