$\"\"$

Consider a line equation $\"\"$ .

Let $\"\"$ .

Substitute $\"\"$ in above the equation.

$\"\"$ .

Let $\"\"$ .

If we take $\"\"$ then parametric equations are $\"\"$ and $\"\"$ for the same line $\"\"$ .

Let $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

If we take $\"\"$ then parametric equations are $\"\"$ and $\"\"$ for the same line $\"\"$ .

Similarly the parametric equations are varied with respect to the values we are considered.

Thus, there are infinitely many sets of parametric equations to describe the one line in $\"\"$ -plane.

$\"\"$

There are infinitely many sets of parametric equations to describe the one line in $\"\"$ -plane.