suppose i have the following curves:
$C_1=\{(t,t+2)|t\in\mathbb{R}\}$
$C_2=\{(t+2,t)|t\in\mathbb{R}\}$
$C_3=\{(t^2+t+1,t^2-t+1)|t\in\mathbb{R}\}$
$C_4=\{(t^2+t+2,t^2-t+2)|t\in\mathbb{R}\}$
define $T$ as the region bounded between the 4 curves, $L:\mathbb{R}^2\rightarrow \mathbb{R}^2$ by $L(p,q)=(p+q,p-q)$ find a set $S\subset \mathbb{R}^2$ such that $L(S)=T$
as a hint i was told to look at $L(t,2+t^2),L(t,1+t^2)$, I found that $L(t,2+t^2)=C_4$ and $L(t,1+t^2)=C_4$
on desmos i found how the curves look and i tried finding the intersection points but that didn't get me anywhere.
any tips on i can approach these types of questions involving parametric curves?