Question

The locus of the mid-points of the parallel chords with slope $m$ of the rectangular hyperbola $xy=c^{2}$ is

• A. $y+mx=0$
• B. $y-mx=0$
• C. $my-x=0$
• D. $my+x=0$

Answer 1

Answer: (A)

$\left(h , k\right),$ then
Equation of $AB$ is $\frac{x}{h}+\frac{y}{k}=2$
$m=-\frac{k}{h}\therefore y=-mx$