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

\frac{80}{9}

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\frac{9}{80}

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9

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80

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Solution

The correct option is A $\frac{80}{9}$
If AFB is focal chord of parabola $y^{2} = 4 x$ and AF and FB are $4$ and $5$ then latus rectum is :
Semi latus rectum $= 2 a = \frac{2 (A F) (F B)}{A F + F B} = \frac{2 (4) (5)}{4 + 5} = \frac{40}{9}$
Latus recutum $= 4 a = 2 (2 a) = \frac{80}{9}$

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