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If $P S Q$ is the focal chord of the parabola $y^2=8 x$ such that $S P=6$. Then the length $S Q$ is
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The correct answer is:
$3$
Since the semi-latus rectum of a parabola is the harmonic mean between the segments of any focal chord of a parabola, therefore $S P, 4, S Q$ are in H.P.
$\Rightarrow 4=2 \cdot \frac{S P \cdot S Q}{S P+S Q}$ $\Rightarrow4=\frac{2(6)(S Q)}{6+S Q} \Rightarrow S Q=3$
$\Rightarrow 4=2 \cdot \frac{S P \cdot S Q}{S P+S Q}$ $\Rightarrow4=\frac{2(6)(S Q)}{6+S Q} \Rightarrow S Q=3$
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