$\"\"$

\

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

\

Eliminate the angular parameter $\"\"$ by solving the parametric equations $\"\"$ and $\"\"$ for $\"\"$ and $\"\"$ .

\

$\"\"$ and $\"\"$

\

$\"\"$ and $\"\"$

\

Pythagorean identity : $\"\"$ .

\

$\"\"$

\

The rectangular equation is $\"\"$ .

\

$\"\"$

\

The rectangular equation $\"\"$ represents an ellipse centered at the origin with vertices at $\"\"$ and $\"\"$ and covertices at $\"\"$ and $\"\"$ .

\

Draw a coordinate plane.

\

Graph the curve $\"\"$ with orientation.

\

Graph :

\

$\"\"$ .

\

Observe the graph :

\

As $\"\"$ varies from $\"\"$ to $\"\"$ , the ellipse is traced out counter clockwise.

\

$\"\"$

\

The rectangular equations is $\"\"$ .

\

Graph :

\

$\"\"$ .