Q. If $b$ and $C$ are the lengths of the segments of any focal chord of a parabola $y^{2} = 4ax$, then the length of the semilatusrectum is
A) $\frac{bc}{b + c}$
B) $\sqrt{bc}$
C) $\frac{b + c}{2}$
D) $\frac{2bc}{b + c}$
Explanation
(d)
Since, the semi latusrectum 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, $l = \frac{2bc}{b + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.