Question

If $PSQ$ is the focal chord of a parabola such that $SP=2$ and $SQ=4$ then the length of the latus rectum is

• A. $\frac{8}{3}$
• B. $\frac{16}{3}$
• C. $\frac{25}{3}$
• D. $\frac{4}{3}$

Answer 1

The correct option is B $\frac{16}{3}$

As we know $SP,2a,SQ$ are in H.P.
$\frac{1}{SP}+\frac{1}{SQ}=\frac{2}{2a}$
$\frac{1}{2}+\frac{1}{4}=\frac{2}{2a}$
$\Rightarrow a=\frac{4}{3}$
Length of latus-rectum is
$4a=\frac{16}{3}$