Solving Parametric Equations: Eliminate t & Find x-y Cartesian Equation

[wuffle]

Hello forum! I have yet another question concerning calculus and the topic we're doing right now is extremely confusing for me.

Homework Statement

Eliminate the parameter from the parametric equations x=3t/(1+t³), y=3t²/(1+t³), and hence find an Cartesian equation in x and y for this
curve.

Homework Equations

The Attempt at a Solution

ummm, i have no idea how to approach this question, i assume with parametric equation you need to express t in terms of y and plug in it another equation where x is defined... however, these two equations are pretty complicated and you can't really express t in terms of y and plug it in another equation, what do you do?

I notice the x and y equations are very similar except that y=t^2 in numerator and I am certain you should use that somehow...but I have no idea how

 

[dextercioby]

So it's y(x) = x t(x), but t(x) can't be expressed in a simple manner, since it should come from a cubic.

 

[wuffle]

So it's y(x) = x t(x), but t(x) can't be expressed in a simple manner, since it should come from a cubic.

I guess...

turns out my x=y^2 was wrong, now I am completely lost.

actually yeah, i just fond out y(x)=x * t(x), i just plugged in some numbers and it turned out y/x=t, what do i do with that?

 

[wuffle]

Still can't get it.

I guess writing it as y(x)=xt(x) works but shouldn't we get rid of t in our equation?

 

[dextercioby]

You should get rid of t, of course, but it ain't easy. To get somewhere, you should first have x and y defined as functions of t on a certain interval, i.e. look for the inverse function t =t(x) only when this exists, i.e. on the set of x's on which the mapping is single valued and well-bahaved.

But then even this can't guarantee you that t=t(x) can be found without solving the cubic with Cardano's formulae.