$\"\"$

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

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Find $\"\"$ .

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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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$\"\"$ .

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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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$\"\"$ .

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

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$\"\"$

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

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$\"\"$

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$\"\"$

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Find the equation of the tangent line at $\"\"$ .

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Here $\"\"$ and $\"\"$ , hence $\"\"$ lies in first quadrant.

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$\"\"$

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$\"\"$ .

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Since $\"\"$ lies in first quadrant, $\"\"$ .

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$\"\"$

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Find the slope of the tangent line $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$ .

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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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Find the equation of the tangent line at $\"\"$ .

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Here $\"\"$ and $\"\"$ , hence $\"\"$ lies in second quadrant.

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$\"\"$

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$\"\"$ .

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Since $\"\"$ lies in second quadrant, $\"\"$ .

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$\"\"$

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Find the slope of the tangent line $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$ .

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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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Find the equation of the tangent line at $\"\"$ .

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Here $\"\"$ and $\"\"$ , hence $\"\"$ lies in first quadrant.

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$\"\"$

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$\"\"$ .

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Since $\"\"$ lies in first quadrant, $\"\"$ .

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$\"\"$

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Find the slope of the tangent line $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$ .

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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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$\"\"$

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

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$\"\"$

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

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

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