# Tricky Parametric equation

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 ?

0rthodontist
Note that x - t = y + t (or just subtract y(t) from x(t)).

Last edited:
Gagle The Terrible said:
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 ?
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.

0rthodontist