If a and c are the segments of a focal chord | vedclass

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(C) The semi-latus rectum of a parabola is the harmonic mean between the segments of any focal chord.Let the segments of the focal chord be $a$ and $c

Vedclass · Accepted Answer

$a, b, c$ are in $H.P.$

Vedclass · Answer

(C) The semi-latus rectum of a parabola is the harmonic mean between the segments of any focal chord.Let the segments of the focal chord be $a$ and $c$,and the semi-latus rectum be $b$.By the property of the focal chord,we have $b = \frac{2ac}{a + c}$.This implies that $\frac{1}{b} = \frac{a + c}{2ac} = \frac{1}{2} \left( \frac{1}{c} + \frac{1}{a} \right)$.Since the reciprocals of $a, b, c$ are in arithmetic progression,$a, b, c$ are in harmonic progression $(H.P.)$.

If $a$ and $c$ are the segments of a focal chord of a parabola and $b$ is the semi-latus rectum,then:

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