Question

If $2$ and $3$ are the lengths of the segments of any focal chord of a parabola $y^2=4ax$ made by the axis of the parabola, then the length of the latus rectum is

• A. $\frac{24}{5}$
• B. $\frac{12}{5}$
• C. $\frac{11}{5}$
• D. $\text{none of these}$

Answer 1

The correct option is A $\frac{24}{5}$

If $2$ and $3$ are lengths of segment of focal chord of parabola $y^2=4ax$
Let $l_1=2,l_2=3$
Semi latus rectum $=2a=\frac{2l_1{l}_2}{l_1+l_2}$
$=\frac{2\left(2\right)\left(3\right)}{2+3}=\frac{12}{5}$
Hence the length of the latusrectum
$=4a=\frac{24}{5}$