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Question

The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is

A
2logy=x21
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B
2logx=y21
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C
2logx=y2+1
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D
2logy=x2+1
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Solution

The correct option is A 2logy=x21
According to the question
dydx=xy1ydy=xdx
On Integrating both sides, We get-
logy=x22+c
Curve passes through (1, 1)
log1=12+c
0=12+c
c=12
logy=x2212
2logy=x21

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