$\"\"$

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The conic equation is

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$\"\"$ .

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$\"\"$

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Use rotational formula to find $\"\"$ .

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

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Substitute $\"\"$ in rotational formulas.

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$\"\"$

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$\"\"$

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And

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in equation $\"\"$ .

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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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The equation of the rotated ellipse in the $\"\"$ -plane is $\"\"$ .