$\"\"$

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

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Rotation equations for $\"\"$ and $\"\"$ :

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

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Substitute $\"\"$ .

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

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

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

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$\"\"$

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

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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 in the $\"\"$ -plane is $\"\"$ .

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$\"\"$

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The equation in the $\"\"$ -plane is $\"\"$ .

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Compare the equation with general conic equation $\"\"$ .

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

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For this equation:

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$\"\"$

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$\"\"$ , the conic is either ellipse or circle.

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The conic has different values of coefficients.

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Therefore, the conic is ellipse.

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$\"\"$

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The equation in the $\"\"$ -plane is $\"\"$ .

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The conic is ellipse.