$\"\"$

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

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(a)

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Graph:

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Graph the parametric equations $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$

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(b)

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Find $\"\"$ , $\"\"$ and $\"\"$ at the point $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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At $\"\"$ , $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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At $\"\"$ , $\"\"$ .

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Find $\"\"$ .

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Parametric form of derivatives: $\"\"$ .

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$\"\"$ .

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Substitute the corresponding values.

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$\"\"$

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At $\"\"$ , $\"\"$ .

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$\"\"$

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(c)

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Find the point $\"\"$ at $\"\"$ .

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At $\"\"$ , $\"\"$ .

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At $\"\"$ , $\"\"$ .

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Point on the curve is $\"\"$ .

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Point slope form of line equation is $\"\"$ .

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

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$\"\"$

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Tangent line equation at $\"\"$ is $\"\"$ .

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$\"\"$

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(d)

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Graph:

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Graph the parametric equations $\"\"$ and $\"\"$ .

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Graph the tangent line $\"\"$ and plot the point $\"\"$ .

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$\"\"$ .

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$\"\"$

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(a)

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Graph of the parametric equations $\"\"$ and $\"\"$ is

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$\"\"$ .

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(b) $\"\"$ , $\"\"$ and $\"\"$ .

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(c) Tangent line equation at $\"\"$ is $\"\"$ .

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(d)

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Graph of the parametric equations $\"\"$ and $\"\"$ and tangent line $\"\"$ is

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$\"\"$ .