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

Step-by-step solution

x^2+y^2= t + 1 t Squaring on both sides, we get x^4+y^4+2 x^2 y^2=t^2+ 1 t^2 +2 aligned t ^2+ 1 t ^2 +2 x^2 y^2= t ^2 & + 1 t ^2 +2 & [ x^4+y^4= t ^2+ 1 t ^2 , given ] aligned aligned & 2 x^2 y^2=2 & x^2 y^2=1 aligned differentiating w.r.t. x , we get aligned & x^2 2 y d y ~d x +2 x y^2=0 & x^2 2 y d y ~d x =-2 x y^2 & d y ~d x = -2 x y^2 2 x^2 y = -y x aligned