The latusrectum of the parabola $ y^{2}=4 a x $, whose focal chord is $ P S Q $, such that $ S P=3 $ and $ S Q=2 $ is given by

Question

The latusrectum of the parabola $ y^{2}=4 a x $, whose focal chord is $ P S Q $, such that $ S P=3 $ and $ S Q=2 $ is given by, $ \frac{24}{5} $, $ \frac{12}{5} $, $ \frac{6}{5} $, $ \frac{1}{5} $

MARKS App · Accepted Answer

Since, the semi latus-rectum of a parabola is the HM of segments of a focal chord. Hence the semi latus rectum is:- = 2 S P . S Q S P + S Q = 2 × 3 × 2 3 + 2 = 12 5 ∴ Latus rectum of the parabola = 24 5

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