$\"\"$

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The polar equation is $\"\"$ and $\"\"$ .

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If the point $\"\"$ has Cartesian coordinates $\"\"$ and polar coordinates $\"\"$ , then $\"\"$ and $\"\"$ .

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Substitute $\"\"$ in polar coordinates.

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$\"\"$ .

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$\"\"$ .

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The slope of the tangent line is derivative of the function.

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Apply chain rule of derivatives : $\"\"$ .

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First 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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Apply product rule of derivatives: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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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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Apply product rule of derivatives: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$ .

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The slope of the tangent line of polar equation $\"\"$ is $\"\"$ .

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$\"\"$

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The curve equation is $\"\"$ .

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Substitute $\"\"$ in polar coordinates.

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$\"\"$ .

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$\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$ .

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The slope of the tangent line of polar equation $\"\"$ is $\"\"$ .

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$\"\"$

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The slope of the tangent line of polar equation $\"\"$ is $\"\"$ .

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The slope of the tangent line of polar equation $\"\"$ is $\"\"$ .

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The product of slopes is

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$\"\"$

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$\"\"$ .

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The tangent lines of $\"\"$ and $\"\"$ are perpendicular to each other.

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Therefore, the curves $\"\"$ and $\"\"$ are perpendicular. \ \

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$\"\"$

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The curves $\"\"$ and $\"\"$ are perpendicular.