Locus of the middle points of the parallel chords with gradient m… - Vidyadip

MCQ

Locus of the middle points of the parallel chords with gradient $m$ of the rectangular hyperbola $xy = c^2 $ is

✓
$y + mx = 0$
B
$y - mx = 0$
C
$my - x = 0$
D
$my + x = 0$

✓

Answer

Correct option: A.

$y + mx = 0$

a
equation of chord with mid point $ (h, k)$ is $\frac{x}{h} + \frac{y}{k}$ $ = 2$ ;

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

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