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If √(1-x²ⁿ)+√(1-y²ⁿ)=a(xⁿ-yⁿ), then the value of (√(1-x²ⁿ) dy)/(√(1-y²ⁿ) dx) is

1. 1
2. x/y
3. xⁿ⁻¹/yⁿ⁻¹
4. None of these

Correct answer: xⁿ⁻¹/yⁿ⁻¹

Solution

The equation given can be differentiated implicitly with respect to both variables, leading to a relationship between the derivatives of x and y. By rearranging the terms and simplifying, we find that the ratio of the derivatives corresponds to the expression xⁿ⁻¹/yⁿ⁻¹, confirming that this is the correct option.

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