Question

Let $PSQ$ be the focal chord of the parabola, $y^2=8x$. If the length of $SP=6$ then, $l\left(SQ\right)$ is equal to $($where $S$ is the focus$)$

• A. $3$
• B. $4$
• C. $6$
• D. None

Answer 1

The correct option is A $3$

Given $SP=6,SL=$ length of semi latus rectum $=4$
We know $SP.SL,SQ$ forms a H.P
$\Rightarrow \frac{2}{SL}=\frac{1}{SP}+\frac{1}{SQ}$
$\Rightarrow \frac{2}{4}=\frac{1}{6}+\frac{1}{SQ}\Rightarrow SQ=3$