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The length of the latus rectum of a parabola whose focal chord $P S Q$ is such that $P S=3$ and $Q S=2$ is
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Verified Answer
The correct answer is:
$\frac{24}{5}$
We know that the length of the semi latus rectum is the harmonic mean of focal radii, so length of the latus rectum
$$
=2\left(\frac{2(P S)(Q S)}{P S+Q S}\right)=2 \times \frac{2 \times 3 \times 2}{3+2}=\frac{24}{5}
$$
$$
=2\left(\frac{2(P S)(Q S)}{P S+Q S}\right)=2 \times \frac{2 \times 3 \times 2}{3+2}=\frac{24}{5}
$$
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