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AP EAMCET2015MathematicsDifferentiation

If x^2+y^2=t+ 1 t and x^4+y^4=t^2+ 1 t^2 , then d y d x is equal to

Options

  1. A- x y
  2. B- y x
  3. C- x^2 y^2
  4. D- y^2 x^2

Correct answer

B. - y x

Step-by-step solution

We have, From Eq. (i), squaring both the sides aligned & (x^2+y^2 )^2= (t+ 1 t )^2 & x^4+y^4+2 x^2 y^2=t^2+ 1 t^2 +2 & .x^4+y^4+2 x^2 y^2=x^4+y^4+2 [using Eq. (ii) ] & 2 x^2 y^2=2 aligned Differentiating w.r.t. x , we get aligned & 2 x y^2+2 x^2 y d y d x =0 & d y d x = -2 x y^2 2 x^2 y =- y x aligned

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