If x^2+y^2= t + 1 t , x^4+y^4= t ^2+ 1 t ^2 , then d y ~d x =

Step-by-step solution

array ll & x^2+y^2= t + 1 t and x^4+y^4= t ^2+ 1 t ^2 & (x^2+y^2 )^2= ( t + 1 t )^2 & x^4+y^4+2 x^2 y^2= t ^2+ 1 t ^2 +2 & t ^2+ 1 t ^2 +2 x^2 y^2= t ^2+ 1 t ^2 +2 & x^2 y ^2=1 & y^2= 1 x^2 array Differentiating w.r.t. x , we get aligned & 2 y ~d y ~d x = -2 x^3 & ~d y ~d x = -1 x^3 y aligned