Question

Locus of the middle points of the parallel chords with gradient $m$ 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

The correct option is A $y+mx=0$

Let middle point of chord is $P(h,k)$

Thus equation of chord with mid point P is, $kx+hy=2hk$

Given slope of this chord is $m$

$\Rightarrow \frac{-k}{h}=m\Rightarrow k+mh=0$

Thus locus of $P(h,k)$ is, $y+mx=0$

Hence, option 'A' is correct.