Question

The latusrectum of a parabola $y^2=4ax$ whose focal chord is $PSQ$ such that $SP=3$ and $SQ=2$, is given by

• A. $\frac{24}{5}$
• B. $\frac{12}{5}$
• C. $\frac{6}{5}$
• D. $\frac{1}{5}$

Answer 1

Answer: (A)

$\frac{24}{5}$

Given that:

$SP=3,SQ=2$

Say the latus rectum is $c$ then

$SP,\frac{c}{2},SQ$ are in $H.P.$

$\frac{1}{3}+\frac{1}{2}=\frac{4}{c}$

$\frac{2+3}{6}=\frac{4}{c}$

$c=\frac{24}{5}.$

Hence the latus rectum is $\frac{24}{5}.$