Question

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 latus rectum is$$.

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

Answer 1

The correct option is D

$\frac{2bc}{\left[b+c\right]}$

Finding the length of the latus rectum:

It is given that $b$ and $c$ are lengths of the segments of any focal chord of the parabola $y^2=4ax$.

If $l$ is the length of the semi latus rectum of the parabola, then

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

$I=\frac{2bc}{\left(b+c\right)}$

The length of latus rectum $=\frac{2bc}{\left(b+c\right)}$

Hence option (D) is Correct.