$\"\"$

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The conic equation is $\"\"$ where $\"\"$ .

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$\"\"$

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Find $\"\"$ and $\"\"$ using rotational formula.

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$\"\"$ .

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Substitute $\"\"$ in the above 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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$\"\"$ .

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Substitute $\"\"$ in equation (1).

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$\"\"$

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$\"\"$ .

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$\"\"$

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