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KCET2013MathematicsApplication of Derivatives

If the length of the subtangent at any point to the curve x y^ n =a is proportional to the abscissa, then n is

Options

  1. Aany non-zero real number
  2. B2
  3. C-2
  4. D1

Correct answer

A. any non-zero real number

Step-by-step solution

Given, curve is x y^ n =a On differentiating w.r.t. x , we get x n y^ n-1 d y d x +y^ n =0 y^ n-1 [x n d y d x +y ]=0 d y d x =- y n x ( y 0) aligned Length of subtangent &= y (d y / d x) &=y ( -n x y )=-n x aligned Since, it is proportional to x . So, n can be any non-zero real number.

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