$\"\"$

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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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Consider $\"\"$ .

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$\"\"$

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Divide equation (2) by equation (1).

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$\"\"$

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The above equation is a equation of stright line passing through $\"\"$ and $\"\"$ .

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Here the interval of $\"\"$ is $\"\"$ .

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So $\"\"$ lies between $\"\"$ and $\"\"$ , and $\"\"$ lies between $\"\"$ and $\"\"$ .

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Therefore, the parametric equations to represent the line segment that joins the points $\"\"$ and $\"\"$ .

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$\"\"$

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(b)

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The points of the line segment from $\"\"$ to $\"\"$ .

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

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Consider $\"\"$ .

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Substitute corresponding values.

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Substitute corresponding values.

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$\"\"$

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

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$\"\"$

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