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# How do I turn the equation of a rotated ellipse into its equation when not rotated?

So let's say I have the equation "4y^2+2xy+2x^2-8x=51". This is a rotated ellipse, so how can I find its equation when it is not rotated, however still has the same vertical and horizontal stretches? Thank you in advance.

### 1 Answer

Relevance

- ted sLv 74 weeks ago
you first find the angle Θ of rotation ....cot 2Θ = b / [ a - c ]...where a ² + b xy + c y² +......then x = x' cos Θ - y ' sin Θ and y = x' sin Θ + y' cos Θ yields : A x'² + C y'² + ....after the substitutions

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