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Formation of a Differential Equation from a General Solution

The D.E of th...

Question

The D.E of the family of rectangular hyperbolas which have the coordinate axes as asymptotes is:

A

x y_{1} + y = 0

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B

x y_{2} + y_{1} = 0

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C

x y_{2} = y

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D

x y_{2} + y = 0

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Solution

The correct option is C $x y_{1} + y = 0$
Equation is $x y = c$
$\Rightarrow x y = c$
$\Rightarrow x y_{1} + y = 0$

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