Step 1:

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The polar equation is $\"\"$ .

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Find the points on the curve where the tangent line is horizontal or vertical.

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Slope of the horizontal tangent line is 0.

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Slope of the vertical tangent line is $\"\"$ .

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Find the slope of the curve.

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Step 2:

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Slope of the tangent line is first derivative of the curve.

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Slope of the parametric equation is

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in the above equation.

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$\"\"$

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Slope of the tangent line is $\"\"$ .

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Step 3:

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Slope of the horizontal tangent line is 0.

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$\"\"$

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$\"\"$

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The general solution of $\"\"$ is $\"\"$ .

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$\"\"$

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If $\"\"$ then $\"\"$ .

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If $\"\"$ then $\"\"$ .

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Now substitute $\"\"$ in polar equation.

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$\"\"$

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Now substitute $\"\"$ in polar equation.

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$\"\"$

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The points on the curve where tangent line is horizontal are $\"\"$ and $\"\"$ .

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Step 4:

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Slope of the vertical tangent line is $\"\"$ .

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$\"\"$

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$\"\"$

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The general solution of $\"\"$ is $\"\"$ .

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$\"\"$

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If $\"\"$ then $\"\"$ .

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If $\"\"$ then $\"\"$ .

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Now substitute $\"\"$ in polar equation.

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$\"\"$

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Now substitute $\"\"$ in polar equation.

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$\"\"$

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The points on the curve where tangent line is vertical are $\"\"$ and $\"\"$ .

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Solution:

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The points on the curve where tangent line is vertical are $\"\"$ and $\"\"$ .

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The points on the curve where tangent line is horizontal are $\"\"$ and $\"\"$ .