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Find the equation of the curve passing t...

Find the equation of the curve passing through (2,1) which has constant sub-tangent.

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We are given that
sub-tangent `=y/((dy)/(dx))=k` (constant)
or `k(dy)/(y)=dx`
Integrating we get, `klogy=x+c`
Given, that curve passes through (2,1) `rArr c=-2`
Hence, the equation of such curve is `klogy=x-2`
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