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  • The lengths of the latus rectum of a parabola whose focal chord <img alt="\ma

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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