Tricky Parametric equation

1. Jul 8, 2006

Gagle The Terrible

I would like to convert these parametric equations into a single
f(x,y) = 0 function.

X(t) = t^2 + t + 1
Y(t) = t^2 - t +1

In fact, what stops me is the imaginary roots of the parametric polynomials.

Is there a way to get around the seemingly impossible explicit solving of the quadratics to isolate either X or Y ?

2. Jul 8, 2006

0rthodontist

Note that x - t = y + t (or just subtract y(t) from x(t)).

Last edited: Jul 8, 2006
3. Jul 8, 2006

d_leet

First note that X - Y = 2t, but also notice that these are both quadratic equations so you can solve one of them or the other to find t in terms of X or Y and then substitute this into X - Y = 2t or the equation for the other variable.

4. Jul 8, 2006

0rthodontist

You just want to substitute t = (x - y) / 2. There's no need to solve any quadratics.

5. Jul 9, 2006

d_leet

Darn, I guess I should have seen that since I did notice that x - y = 2t.