$\"\"$

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

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$\"\"$

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The general form of a conic is $\"\"$ .

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

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Find $\"\"$ .

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$\"\"$

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The conic is an ellipse.

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$\"\"$

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The angle is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in the above equation.

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$\"\"$

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Assume that the angle lies on second quadrant.

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$\"\"$

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Observe the diagram :

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$\"\"$ .

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$\"\"$

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

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Half angle identity : $\"\"$ .

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$\"\"$

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Half angle identity : $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Find equations for $\"\"$ and $\"\"$ .

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$\"\"$ .

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

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$\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The standard form of equation is $\"\"$ .