Question

If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2=4ax$, then length of the semi-latus rectum is

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

Answer 1

Answer: (C)

$\frac{2bc}{b+c}$

We know that, the semi latus-rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola.

Given that, $b$ and $c$ are lengths of the segments of any focal chord of the parabola $y^2=4ax$

So, Let $l$ is the length of semi-latus rectum of the parabola.

Then,$\frac{1}{b}+\frac{1}{c}=\frac{2}{l}$

$\Rightarrow l=\frac{2bc}{b+c}$

Hence, length of semi-latus-rectum$=\frac{2bc}{b+c}$