If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2=4 a x$, then the length…
If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2=4 a x$, then the length of the semi-latus rectum is :
$\frac{b c}{b+c}$
$\sqrt{b c}$
$\frac{b+c}{2}$
$\frac{2 b c}{b+c}$
Solution
Since the semi latus rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola. $\therefore l$ is the harmonic mean between $b$ and $c$. Hence,
$l=\frac{2 b c}{b+c}$