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Length of Latus Rectum

If AFB is a f...

Question

If AFB is a focal chord of the parabola $y^{2} = 4 a x$ and AF = 4, FB = 5, then the latus-rectum of the parabola is equal to

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Solution

The correct option is A

FA = 4, FB = 5

We know that $\frac{1}{a} = \frac{1}{A F} + \frac{1}{F B}$
$\Rightarrow a = \frac{20}{9} \Rightarrow 4 a = \frac{80}{9},$

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