Answer
The different sets of parametric equation are:
$ x=t\text{,}\,\,y={{t}^{2}}+4\,\,\text{ and }\,\,x=t+1\text{,}\,\,y={{t}^{2}}+2t+5$
(other answers are possible.)
Work Step by Step
Let us assume $ x=t $,
Then, $ y={{t}^{2}}+4$
The solution set for y remains the same for both negative and positive values.
Let $ x=t+1$
Now, $\begin{align}
& y={{(t+1)}^{2}}+4 \\
& y={{t}^{2}}+2t+1+4 \\
& y={{t}^{2}}+2t+5 \\
\end{align}$
The solution set for y remains the same for both negative and positive values.
Note that many different sets of parametric equations are possible. Choose any two from them. Thus, $ x=t\text{,}\,\,y={{t}^{2}}+4\,\,\text{ and }\,\,x=t+1\text{,}\,\,y={{t}^{2}}+2t+5$ are two different sets of parametric equations.
