$\"\"$

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The eccentricity of a conic is $\"\"$ .

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Vertices of the conic is at $\"\"$ and $\"\"$ .

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Since the eccentricity is $\"\"$ , the conic is hyperbola.

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Center is the mid point of the two vertices.

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Therefore, the center of the ellipse is at $\"\"$ .

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Therefore the directrix will be in the right side of the pole at $\"\"$ .

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The polar equation of the conic with the directrix is $\"\"$ .

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$\"\"$

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Find the value of $\"\"$ :

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The vertex $\"\"$ has polar coordinates $\"\"$ .

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

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Susbtitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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Susbtitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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The standard form of polar equation is : $\"\"$ .

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

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$\"\"$

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Substitute $\"\"$ , $\"\"$ in $\"\"$ .

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$\"\"$ .

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Therefore, the polar equation of the conic is $\"\"$ and directrix is $\"\"$ . $\"\"$

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Graph:

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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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$\"\"$

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The polar equation is $\"\"$ .

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Graph :

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$\"\"$