$\"\"$

The parametric equations of an ellipse are $\"\"$ and $\"\"$ .

Eliminate the parameter $\"\"$ .

Consider $\"\"$ .

$\"\"$

Consider $\"\"$ .

$\"\"$

Pythagorean identity : $\"\"$ .

Substitute $\"\"$ and $\"\"$ .

$\"\"$

The standard form of an ellipse equation is $\"\"$ with center $\"\"$ .

$\"\"$

The standard form of an ellipse equation is $\"\"$ .