Find the length of the latus rectum of a para | vedclass

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(A) For a parabola,the length of the semi-latus rectum is the harmonic mean of the segments of any focal chord.Let $l$ be the semi-latus rectum.Then,$

Vedclass · Accepted Answer

$24/5$

Vedclass · Answer

(A) For a parabola,the length of the semi-latus rectum is the harmonic mean of the segments of any focal chord.Let $l$ be the semi-latus rectum.Then,$\frac{1}{SP} + \frac{1}{SQ} = \frac{2}{l}$.Given $SP = 3$ and $SQ = 2$,we have:$\frac{1}{3} + \frac{1}{2} = \frac{2}{l}$$\frac{5}{6} = \frac{2}{l}$$l = \frac{12}{5}$.The length of the latus rectum is $2l = 2 	imes \frac{12}{5} = \frac{24}{5}$.

Find the length of the latus rectum of a parabola if $PSQ$ is a focal chord such that $SP = 3$ and $SQ = 2$.

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