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Focal Chord

The sum of th...

Question

The sum of the reciprocals of the focal distance of a focal chord $P Q$ of $y^{2} = 4 a x$ is

$a$

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$\frac{1}{a}$

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$2 a$

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$\frac{1}{2 a}$

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Solution

The correct option is B
$\frac{1}{a}$

Explanation for the correct option:
The ends of the latus rectum are $(a, 2 a), (a, - 2 a)$
The total length of focal chord = $4 a$
Half length = $2 a$
The sum of reciprocals of the focal lengths $= \frac{1}{2 a} + \frac{1}{2 a} = \frac{1}{a}$
Hence, the correct option is option(B).

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