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Manipal MET2014MathematicsApplication of Derivatives

The equation of the tangent to the curve ( x a )^n+ ( y b )^n=2 at (a, b) is

Options

  1. Ax a + y b =2
  2. Bx a + y b = 1 2
  3. Cx b - y a =2
  4. Da x+b y=2

Correct answer

A. x a + y b =2

Step-by-step solution

The given curve is ( x a )^n+ ( y b )^n=2 aligned & n ( x a )^ n-1 1 a +n ( y b )^ n-1 1 b d y d x =0 & d y d x =- b a ( x a )^ n-1 ( y b )^ n-1 aligned At (a, b), d y d x =- b a (1)^ n-1 (1)^ n-1 =- b a The tangent at (a, b) is array cc & y-b=- b a (x-a) & a y-a b=-b x+a b & b x+a y=2 a b & x a + y b =2 array

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