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).