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Let x^k+y^k =a^k, (a,k gt 0) and (dy)/(d...

Let `x^k+y^k =a^k, (a,k gt 0)` and `(dy)/(dx) +(y/x)^(5//3)=0` , then k=

A

`1/3`

B

`2/3`

C

`-1/3`

D

`-2/3`

Text Solution

Verified by Experts

The correct Answer is:
D
`kx^(k-1) + ky^(k-1) (dy)/(dx)=0`
`(dy)/(dx)=-(k(x^(k-1)))/(k(y^(k-1))) rArr (dy)/(dx) = - (y/x)^(1-k)`
Now by comparing `1-k=5/3`
`k=1-5/3 rArr k=-2/3`
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