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if sqrt(1-x^2)+sqrt(1-y^2)=a(x-y),prove that dy/dx=sqrt(1-y^2/1-x^2).
Differentiating the given equation with respect to x, we get,
- x / sqrt(1 - x^2) - [y / sqrt(1 - y^2] dy/dx = a (1 - dy/dx)
=> [a - y / sqrt(1 - y^2)] dy/dx = a + x / sqrt(1 - x^2)
=> [a sqrt(1 - y^2) - y] / sqrt(1 - y^2) dy/dx = [a sqrt(1 - x^2) + x] / sqrt(1 - x^2) ... ( 1 )

Now, in the above equation (in both sides) substitute the value of a from the given equation. Thereafter, you will easily get the required value for dy/dx.
Answered by | 15 Aug, 2012, 10:13: PM

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