$\"\"$

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The rectangular equation is $\"\"$ .

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Rewrite the equation: $\"\"$ .

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The equation is in the form of stan`dard equation of ellipse: $\"\"$ .

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Here, $\"\"$ , $\"\"$ and $\"\"$ .

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For an ellipse $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The eccentricity is $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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The eccentricity of ellipse is $\"\"$ .

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$\"\"$

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The directrix of horizontal ellipse is $\"\"$ .

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

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$\"\"$

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$\"\"$

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

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Let us consider the directrix is $\"\"$ .

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If the directrix is a horizontal line $\"\"$ , then the polar equation of the conic is $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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The polar equation is $\"\"$ .

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$\"\"$

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The polar equation is $\"\"$ .