Question

Find the latus rectum of a parabola whose focal chord $PSQ$ is such that $SP=3$ and $SQ=2.$

• A. $\frac{24}{5}$
• B. $\frac{12}{5}$
• C. $\frac{8}{5}$
• D. $\frac{6}{5}$

Answer 1

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

R.E.F image

$PS=3$

$PQ=2$

$Q,C/2,b$ are in HP

$\frac{1}{a}+\frac{1}{b}=\frac{4}{c}$

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

$\Rightarrow \frac{5}{6}=\frac{4}{c}$

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