Answer
Taking different values of t for both equations of x and y, the graph of the parametric equations can be plotted.
Work Step by Step
We know that the parametric equations are the equations having a common variable in both x and y. And by taking the values of t manually, one can get the values of x and y separately. And the corresponding points can be plotted to get a graph of the given parametric equations.
For example:
If the parametric equations are as given below:
$\begin{align}
& x=t \\
& y=2{{t}^{2}} \\
\end{align}$
Take the values of t manually and compute the values of x and y as given below:
For $ t=1$
$\begin{align}
& x=t \\
& =1
\end{align}$
$\begin{align}
& y=2{{t}^{2}} \\
& =2{{\left( 1 \right)}^{2}} \\
& =2
\end{align}$
Similarly, for $ t=2$
$\begin{align}
& x=t \\
& =2
\end{align}$
$\begin{align}
& y=2{{t}^{2}} \\
& =2{{\left( 2 \right)}^{2}} \\
& =8
\end{align}$
And take some more values of t and get the values of x and y as given below:
$\begin{align}
& t=3 \\
& x=3 \\
& y=18 \\
\end{align}$
$\begin{align}
& t=4 \\
& x=4 \\
& y=32 \\
\end{align}$
Thus, take these values of x and y to plot the graph as drawn below:
