$\"\"$

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

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

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

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

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Pythagorean identity : $\"\"$ .

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$\"\"$

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The rectungular equation is $\"\"$ .

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$\"\"$

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

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Draw a coordinate plane.

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

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Graph :

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$\"\"$ .

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Observe the graph :

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

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$\"\"$

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The rectangular equations is $\"\"$ .

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Graph :

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$\"\"$ .