If PSQ is the focal chord of the parabola y^2 | vedclass

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(C) For a parabola $y^2 = 4ax$,the semi-latus rectum $l = 2a$ is the harmonic mean of the segments of any focal chord $PSQ$.Given $y^2 = 8x$,we have $

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$3$

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(C) For a parabola $y^2 = 4ax$,the semi-latus rectum $l = 2a$ is the harmonic mean of the segments of any focal chord $PSQ$.Given $y^2 = 8x$,we have $4a = 8$,so $a = 2$. Thus,the semi-latus rectum $l = 2a = 4$.Since $SP, l, SQ$ are in Harmonic Progression $(H.P.)$,we have:$l = \frac{2(SP)(SQ)}{SP + SQ}$Substituting the values $SP = 6$ and $l = 4$:$4 = \frac{2(6)(SQ)}{6 + SQ}$$4 = \frac{12(SQ)}{6 + SQ}$$4(6 + SQ) = 12(SQ)$$24 + 4(SQ) = 12(SQ)$$8(SQ) = 24$$SQ = 3$.

If $PSQ$ is the focal chord of the parabola $y^2 = 8x$ such that $SP = 6$,then the length $SQ$ is:

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