$\"\"$

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(a)

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

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Consider $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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(b)

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

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Consider $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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(c)

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

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$ +

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$\"\"$

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Observe the graphs (a), (b) and (c):

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The curves from part (a), (b) and (c) are the same $\"\"$ .

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The curves from (b) and (c) do not exist for $\"\"$ . It is because $\"\"$ cannot negative for (b) and (c).

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The direction of arrows are different for (a) and (c), but same for (a) and (b).

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$\"\"$

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The curve $\"\"$ is generated in (a).

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In (b), only the portion with $\"\"$ is generated, and in (c) only the portion with $\"\"$ is generated.