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AP EAMCET20228 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

The sum of the intercepts made by a tangent drawn to the curve ( x a )^n+ ( y b )^n=2 at (a, b) on the coordinate axes is

Options

  1. Aa+b
  2. Ba^2+b^2
  3. C2(a-b)
  4. D2(a+b)

Correct answer

D. 2(a+b)

Step-by-step solution

Curve it :- ( x a )^ n + ( y b )^ n =2 Let we assume that a =1, ~b =2 Eqn of curve is :- x ^ n + ( y 2 )^ n =2 aligned & Now d y d x = -2^n x^ n-1 y^ n-1 & At (a, b)=(1,2) & ( d y d x )_ (1,2) = -2^n a^ n-1 b^ n-1 = (-2^n ) 1 2^ n-1 =-2^ n-n+1 =-2 aligned Eqn of tangent of the curve is:- y-2=-2 x+2 2 x+y=4 x 2 + y 4 =1 sum of interupt is :- 2+4=6 Check by options to put a =1, ~b =2 options d is satisfied.

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