$\"\"$

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The conic equation is $\"\"$ and the rotation angle is $\"\"$ .

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Use rotational formulas to find $\"\"$ and $\"\"$ .

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Rotational formulas :

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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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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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Draw a coordinate plane.

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Graph the hyperbola $\"\"$ .

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Graph :

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$\"\"$ .

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$\"\"$

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

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Graph :

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$\"\"$ .