If $2$ and $3$ are the length of the segments of any focal chord of a parabola $y^{2} = 4 a x$ , then value of $2 a$ is

\frac{13}{5}

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\frac{12}{5}

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\frac{11}{5}

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none of these

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Solution

The correct option is C $\frac{12}{5}$
If $2$ and $3$ are lengths of focal chord of parabola $y^{2} = 4 a x$ then 2a is :
Let $l_{1} = 2 l_{2} = 3$
Semi latus rectum $= 2 a = \frac{2 l_{1} l_{2}}{l_{1} + l_{2}}$
$= \frac{2 (2) (3)}{2 + 3} = \frac{12}{5}$

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Semi latus rectum of the parabola $y^{2} = 4 a x$ , is the _____ mean between segments of any focal chord of the parabola.

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