Isolating $t$ on a parametric function

Question

I have to plot the graph of $$\gamma(t)=(4t^2-4t,1-4t^2)$$ for $t\in\mathbb{R}$.

I tried to isolate $t$ in $x=4t^{2}-4t$ (or for $y=1-4t^2$), but in this case, I got something with square root. Is there a better way to do this?

Answer 1

Hint. Eliminate $t$ and get that $$ {x}^{2}-2\,xy+{y}^{2}+2\,x+2\,y-3=0. $$