(a)

The parametric equations are and .

Eliminate the parameter :

Consider .

Consider .

Pythagorean identity:

Substitute  and  in above equation.

.

Compare the above equation with standard form of ellipse .

Center: .

.

Thus, the graph of the equation represents an ellipse.

Graph the ellipse.

Graph the equation .

Plot the center point .

Plot the focus points and

.

Plot the vertex points and .

Plot the two points above and below the center and

.

Note that that elliptic curve is traced out counter clock wise as varies from . \ \

From (a)

The rectangular equation  is .

Observe the graph of the equation, the domain set is .

(a)

The graph the parametric equations and .