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KCET2012MathematicsApplication of Derivatives

Length of the subtangent at (x₁, y₁ ) on x^ n y^ m =a^ m+n , m, n>0 , is

Options

  1. An m x₁
  2. Bm n | x ₁ |
  3. Cn m | y ₁ |
  4. Dn m | x ₁ |

Correct answer

B. m n | x ₁ |

Step-by-step solution

Given, x^ n y^ m =a^ m+n , m, n>0 Taking logarithm on both sides, we get gathered (x^ n y^ m )= a^ m+n x^ n + y^ m =(m+n) a n x+m y=(m+n) a gathered On differentiating Eq. (i) w.r.t. ' x ', we get n x + m y dy dx =0 m y dy dx =- n x dy dx =- ( n m ) ( y x ) Length of subtangent = y d y / d x = y - ( n m ) ( y x ) = -m x n Length of subtangent at ( x ₁, y ₁ )= m n | x ₁ |

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