$\"\"$

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The vector line equation is $\"\"$ .

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

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The parametric equations of a line :

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

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$\"\"$

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The parametric equations are $\"\"$ and the point is $\"\"$ .

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Substitute the point $\"\"$ in $\"\"$ .

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$\"\"$

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The point $\"\"$ is corresponds to $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to t.

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$\"\"$

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Substitute $\"\"$ in above equation.

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$\"\"$

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Write the vector notation in component form.

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$\"\"$

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The equation of a tangent line passing through the point $\"\"$ is

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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 $\"\"$ .