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Question

The subtangent at any point of the curve xmyn=am+n varies as

A
(abscissa)2
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B
(abscissa)3
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C
abscissa
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D
ordinate
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Solution

The correct option is D abscissa
We have, xmyn=am+n
Taking logarithm on both sides, we get
mlogx+nlogy=(m+n)loga
Differentiating both sides w.r.t. x, we get
mx+nydydx=0
dxdy=nxmy
Subtangent =ydxdy=nxmx

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