Question

If $b,k$ are the intercepts of the focal chord of $y^2=4ax$, $a\ne b$ then $k$ is

• A. $\frac{ab}{a-b}$
• B. $\frac{ab}{b-a}$
• C. $\frac{2ab}{b-a}$
• D. $\frac{2ab}{a-b}$

Answer 1

The correct option is B $\frac{ab}{b-a}$

$SP=b,SQ=k$

These are the segments of focal chord

By focal chord property
$\frac{1}{SP}+\frac{1}{SQ}=\frac{1}{a}$
$\Rightarrow \frac{1}{b}+\frac{1}{k}=\frac{1}{a}$
$\Rightarrow k=\frac{ab}{b-a}$