$\"\"$

It is because the domain of parametric equations are restricted over the range of $\"\"$ and $\"\"$ .

Consider the set of parametric equations $\"\"$ , $\"\"$ and $\"\"$ , $\"\"$ .

The graph of the parametric equations $\"\"$ and $\"\"$ is a complete circle, where as the graph of the parametric equations $\"\"$ and $\"\"$ is a quarter circle.

Reason:

For parametric equations $\"\"$ and $\"\"$ , $\"\"$ is defined for all real values.

For parametric equations $\"\"$ and $\"\"$ , $\"\"$ restricts its domain such that $\"\"$ .

$\"\"$

The domain of parametric equations are restricted over the range of $\"\"$ and $\"\"$ .