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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Hyperbola

NTA Abhyas 2020 · Mathematics · Hyperbola

The locus of the mid-points of the parallel chords with slope m of...

The locus of the mid-points of the parallel chords with slope

m

of the rectangular hyperbola

xy = c^{2}

is

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

Options

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

Correct answer

A. $y + mx = 0$

Step-by-step solution

Let, the mid-point is

\left(h, k\right),

then
Equation of

AB

is~

\dfrac{x}{h} + \dfrac{y}{k} = 2

m = - \dfrac{k}{h} ∴ y = - mx

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