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Question

The equation of the curve through point 1,0 which satisfies the differential equation 1+y2dx-xydy=0 is


A

x2+y2=4

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B

x2-y2=1

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C

2x2+y2=2

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D

None of these

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Solution

The correct option is B

x2-y2=1


Explanation for correct option:

Given equation of the curve,

1+y2dx-xydy=0dxx-y1+y2dy=0logx2-12log1+y2=constantlogx2-log1+y2=logCx2=C1+y2

The equation of curve passes through point 1,0

Putting 1,0 in the equation,

x2=C1+y2

1=C1+0C=1

Put the value of constant in the equation,x2=C1+y2

We get,

x2-y2=1

Hence, the correct answer is option B.


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