Consider the algebraic curve given by:

   x = 3*t^2/(t^2+1),  y = t^3/(t^2+1)^2   [*]

You can view this curve in Maple by typing:

plot( [3*t^2/(t^2+1),  t^3/(t^2+1)^2, t=-1000..1000]
  ,numpoints=1000);

Find a polynomial equation F(x,y) for this curve.




Hint:  We want: one equation F(x,y)=0 in two variables.
Given in [*] are:

A)   One more equation than what we want.
B)   One more variable than what we want.

And we've discussed in class what you have to do
in general whenever we have a situation with A) and B).