Answer
1) $x=t; y=t^2+1,-\infty\lt t\lt \infty$
2) $x=-t; y=t^2+1,-\infty\lt t\lt \infty$
Work Step by Step
We are given the rectangular equation:
$y=x^2+1$
One set of parametric equations is:
$\begin{cases}
x=t\\
y=t^2+1
\end{cases}$
with $-\infty\lt t\lt \infty$
Another set of parametric equations is:
$\begin{cases}
x=-t\\
y=t^2+1
\end{cases}$
with $-\infty\lt t\lt \infty$
