$\"\"$

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

Rewrite the equations.

$\"\"$

The sum of there squares are equal

$\"\"$

Trigonometric identity : $\"\"$ .

$\"\"$

The above equation is in form of general form of ellipse.

So the particle moves in elliptical path.

$\"\"$

Draw a table for different values of $\"\"$ ranging from $\"\"$ .

Determine the direction of the curve.

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

Graph:

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

$\"\"$

Observe the graph:

From $\"\"$ to $\"\"$ , the elipse does not completes it first revolution in clockwise.

The particle moves counter clockwise around the elliptical path.

$\"\"$

The particle moves counter clockwise around the elliptical path.

The equation is $\"\"$ .