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
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
$\frac{24}{5}$
$\frac{12}{5}$
$\frac{6}{5}$
$\frac{12}{10}$
Solution
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}
$