The locus of the mid-points of the parallel chords with slope m of the rectangular hyperbola xy=c2 is

Question

The locus of the mid-points of the parallel chords with slope m of the rectangular hyperbola xy=c2 is (A) y+mx=0 (B) y-mx=0 (C) my-x=0 (D) my+x=0

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-qrhgbxy4nncj.png" /> (h , k), then Equation of AB is (x/h)+(y/k)=2 m=-(k/h)∴ y=-mx

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

$y + m x = 0$

$y - m x = 0$

$m y - x = 0$

$m y + x = 0$

$(h, k),$ then
Equation of $A B$ is $\frac{x}{h} + \frac{y}{k} = 2$
$m = - \frac{k}{h} ∴ y = - m x$

Q. The locus of the mid-points of the parallel chords with slope m of the rectangular hyperbola xy=c2 is

y+mx=0

y−mx=0

my−x=0

my+x=0