If b and c are lengths of the segments of any focal chord of the parabola $y^{2} = 4 a x,$ then write the lengths of its latus-rectum.

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Solution

We know that,semi latus-rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola.

Given that, b and c are length of the segments of any focal chord of the parabola $y^{2} = 4 a x$

$\frac{1}{b} + \frac{1}{c} = \frac{1}{a}$

$a = \frac{b c}{b + c}$

Length of latus rectum is 4a which is $\frac{4 b c}{b + c}$

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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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