$\"\"$

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The polar equation is $\"\"$ .

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Analyze the polar equation.

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For the polar equation $\"\"$ , eccentricity $\"\"$ and directrix $\"\"$ .

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$\"\"$ .

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The eccentricity and the form of the equation determine that it is a parabola that opens vertically

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with focus at the pole and directrix $\"\"$ .

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The general equation of such a parabola in rectangular form is $\"\"$ .

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$\"\"$

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Determine the values for $\"\"$ and $\"\"$ .

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To determine the values graph the polar equation $\"\"$ .

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(1) Draw the coordinate plane.

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(2) Graph the polar equation $\"\"$ .

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Graph :

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$\"\"$

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Observe the Graph :

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The vertex lies between the focus $\"\"$ and directrix of the parabola occuring when $\"\"$ .

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Evaluating the function at the value the vertex lies at the polar coordinates $\"\"$ ,which corresponds to the rectangular coordinates $\"\"$ .

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Therefore, $\"\"$ , the distance $\"\"$ from the vertex at $\"\"$ to the focus at

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$\"\"$ is $\"\"$ .

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$\"\"$

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Substiute the values $\"\"$ and $\"\"$ in the standard form $\"\"$ .

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$\"\"$

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$\"\"$

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The rectangular form of the equation is $\"\"$ .