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The lengths of the latus rectum of a parabola $\mathrm{y^2=4 a x}$ whose focal chord $\mathrm{P S Q}$ is such that $\mathrm{S P=3}$ and $\mathrm{S Q=2}$ is given by
Option: 1
$\frac{6}{5}$

Option: 2
$\frac{12}{5}$

Option: 3
$\frac{24}{5}$

Option: 4
$\frac{4}{5}$

Answers (1)

For any focal chord $\mathrm{ P S Q}$ of $\mathrm{ y^2=4 a x,}$

$\mathrm{ P S, 2 a, S Q}$ are in H.P.............. (standard result)

Or $\mathrm{ 3,2 a, S Q}$ are in H.P.

The condition is

$\mathrm{ \frac{1}{3}+\frac{1}{2}=\frac{2}{2 a} }$

Or $\mathrm{ a=\frac{6}{3+2}=\frac{6}{5}}$

$\mathrm{ \therefore \quad}$ length of L.R. $\mathrm{ =4 a=\frac{24}{5}}$

The answer is (c)

Posted by

Ramraj Saini

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