COMEDK2013MathematicsApplication of Derivatives

For the curve y^ n =a^ n-1 x if the subnormal at any point is a constant, then n is equal to

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Correct answer

B. 2

Step-by-step solution

We have, y^ n =a^ n-1 x n y^ n-1 d y d x =a^ n-1 y^ n-1 d y d x = 1 n a^ n-1 d y d x = 1 n a^ n-1 y^ 1-n Length of the subnormal = |y d y d x | = |y 1 n a^ n-1 y^ 1-n | = | 1 n a^ n-1 y^ 2-n | 2-n=0 n=2

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