Step 1:

(a)

The parametric equations are $\"\"$ and $\"\"$ and interval of graph is $\"\"$ .

Construct a table for different values of t.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Graph:

Draw the coordinate plane.

Plot the point obtained from the table.

Connect the points to a smooth curve.

$\"\"$

Observe the graph:

From $\"\"$ to $\"\"$ , the ellipse completes it first revolution in clockwise.

Step 2:

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

Consider $\"\"$ .

$\"\"$

Consider $\"\"$ .

$\"\"$

Trigonometric identities : $\"\"$ .

$\"\"$

Rectangular equation of the curve is $\"\"$ .

Solution:

Graph of the curve is

$\"\"$

Rectangular equation of the curve is $\"\"$ .