parametric equation

From x=(1-t^2)/(1+t^2)
(1+t^2)x=(1-t^2)
(1+x)t^2=1-x
So t^2=(1-x)/(1+x) and t=√(1-x)/(1+x),
substitute into y=2t/(1+t^2),
y
=2t/(1+t^2)
=2[√(1-x)/(1+x)]/[2/(1+x)]
=√(1-x)(1+x)
We get x^2+y^2=1 and this is the equation in x and y by eliminating t from the parametric equation