Question

If $PSQ$ is the focal chord of the parabola $y^2=8x$ such that $SP=6$. Then the length of $SQ$ is

• A. $6$
• B. $4$
• C. $3$
• D. None of these

Answer 1

The correct option is C $3$

Since the semi-latus rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola, $SP,4,SQ$ are in $H.P.$ Therefore,
$4=\frac{2SP\times SQ}{SP+SQ}$
$\Rightarrow 4=\frac{2\left(6\right)\left(SQ\right)}{6+SQ}$
$\Rightarrow 24+4\left(SQ\right)=12\left(SQ\right)$
$\Rightarrow SQ=3$