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Question

If the length of the sub-tangent at any point to the curve xyn=a is proportional to the abscissa, then 'n' is ______.

A
Any non-zero real number
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B
2
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C
2
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D
1
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Solution

The correct option is A Any non-zero real number
Length of the sub-tangent is given by ydydx
For the curve xyn=a, differentiating both sides w.r.t x, we have
nxyn1dydx+yn=0
dydx=ynx
sub-tangent =ydydx
=yynx
=nx
Thus, for any non-zero real number n, the length of sub-tangent will be proportional to the abscissa.

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