If x= 1-t² 1+t² and y= 2 a t 1+t² , then d y d x is equal to

Step-by-step solution

Given, x= 1-t² 1+t² and y= 2 a t 1+t² On differentiating w.r.t. t , respectively, we get aligned d x d t &= (1+t² )(0-2 t)- (1-t² )(0+2 t) (1+t² )² &= -4 t (1+t² )² aligned and d y d t = (1+t² ) 2 a-2 a t(2 t) (1+t² )² = 2 a (1-t² ) (1+t² )² d y d x = d y / d t d x / d t = a (1-t² ) -2 t d y d x = a (t²-1 ) 2 t