Finding the Cartesian equation for a set of parametric equations

I'm trying to solve this problem, but I am having trouble. Can someone give me some pointers?

A curve is defined by the parametric equations:

x = 2t / (1 + t^2)

y = (1 - t^2) / (1 + t^2)

By considering the expression x^2 + y^2, eliminate the parameter *t* to obtain the Cartesian (x-y) equation of the curve.

Thanks

Re: Finding the Cartesian equation for a set of parametric equations

so ... what did you determine for the expression in terms of t ?

Re: Finding the Cartesian equation for a set of parametric equations

This is the equation I formed: x^2 + y^2 = (4t^2 - t^4 + 1) / (1 + t^4). I don't know how to eliminate *t* from this point.

Re: Finding the Cartesian equation for a set of parametric equations

first off, note that ...

try adding again ...

Re: Finding the Cartesian equation for a set of parametric equations

Oops, stupid error! Ok, got it now. The ratio cancels out and I get *x*^{2} + y^{2} = 1. Many thanks.

Re: Finding the Cartesian equation for a set of parametric equations

Hello, everyone!

This problem (and solution) involves a paradox.

Paramtric equations: .

Cartesian equation: .

From [3], we have a circle with center at the Origin and radius 1.

. . It has -intercepts and -intercepts

Let's determine the intercepts using the parametric equations.

For -intercepts, let

Substitute into [1]: .

The -intercepts are: .

For -intercepts, let

Substitute into [2]: .

The -intercept is . . . There is only one!

Where is the *other* -intercept?