$\"\"$

The parametric equations are $\"\"$ and $\"\"$ .

Eliminate parameter $\"\"$ .

Consider $\"\"$

$\"\"$

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

$\"\"$

Rewrite the above equation as $\"\"$ .

$\"\"$

$\"\"$ .

The rectangular equation is $\"\"$ .

Since the logarithm of a negative number is not defined, the domain restriction is $\"\"$ .

$\"\"$

The rectangular equation is $\"\"$ .

The domain restriction is $\"\"$ .