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

(a)

Construct a table for different values of $\"\"$ .

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

Graph:

Draw the coordinate plane.

Plot the point obtained from the table.

Connect the points to a smooth curve.

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Observe the graph:

From $\"\"$ to $\"\"$ , the ellipse completes it quater revolution in anticlockwise.

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

Consider $\"\"$ .

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Consider $\"\"$ .

Trigonometric identities : $\"\"$ .

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$\"\"$ .

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

Graph of the curve is

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