If ` log _(10) ((x^(2) - y^(2))/(x^(2) + y^(2))) = 2 , " then" (dy)/(dx) ` is equal to

Options

A. `- (99x)/(101 y)`
B. `(99x)/(101y)`
C. `- (99y)/(101 x)`
D. `(99 y)/(101 x)`

Answer

A

Explanation

Given , `log_(10) ((x^(2) -y^(2))/(x^(2) +y^(2))) = 2 `
` rArr ((x^(2) -y^(2))/(x^(2) +y^(2))) = 10^(2)`
` rArr x^(2) y^(2) = 100 (x^(2) + y^(2))`
On differentiating both sides ,we get
`2x - 2y (dy)/(dx) = 100(2x + 2y (dy)/(dx))`
` rArr x-y(dy)/(dx) = 100 x + 100y (dy)/(dx)`
`rArr 101y(dy)/(dx) = -99x `
` rArr (dy)/(dx) = (-99x)/(101y)` .