Question

If $b$ and $c$ are the lengths of the scgments of any focal chord of a parabola $y^{2}=4 a x$, then the length of the semi-latus rectum is :

• A. $\frac{b c}{b+c}$
• B. $\sqrt{b c}$
• C. $\frac{b+c}{2}$
• D. $\frac{2 b c}{b+c}$

Answer 1

Answer: (D)

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, $l=\frac{2 b c}{b+c}$