PQ is any focal chord of the parabola y^2=32x | vedclass

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(C) The given equation of the parabola is $y^2=32x$.Comparing this with the standard form $y^2=4ax$,we get $4a=32$,which implies $a=8$.The length of a

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$32$

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(C) The given equation of the parabola is $y^2=32x$.Comparing this with the standard form $y^2=4ax$,we get $4a=32$,which implies $a=8$.The length of a focal chord of a parabola $y^2=4ax$ is given by $L = a(t + \frac{1}{t})^2$,where $t$ is the parameter of one end of the chord.The minimum length of a focal chord is the length of the latus rectum,which is $4a$.Therefore,the minimum length $= 4 	imes 8 = 32 	ext{ units}$.Thus,the length of $PQ$ can never be less than $32$ units.

$PQ$ is any focal chord of the parabola $y^2=32x$. The length of $PQ$ can never be less than: ............ $unit$

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