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If sqrt(1-x^(2)) + sqrt(1-y^(2))=a(x-y),...

If `sqrt(1-x^(2)) + sqrt(1-y^(2))=a(x-y)`, then prove that `(dy)/(dx) = sqrt((1-y^(2))/(1-x^(2)))`

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AI Generated Solution

To prove that \(\frac{dy}{dx} = \sqrt{\frac{1 - y^2}{1 - x^2}}\) given the equation \(\sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y)\), we can follow these steps: ### Step 1: Rewrite the equation We start with the given equation: \[ \sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y) \] ...
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