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

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

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$3$

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

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

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