Is there a way to find the parameters $$A, B, \alpha, x_0, y_0$$ for the ellipse formula $$\frac{(x \cos\alpha+y\sin\alpha-x_0\cos\alpha-y_0\sin\alpha)^2}{A^2}+\frac{(-x \sin\alpha+y\cos\alpha+x_0\sin\alpha-y_0\cos\alpha)^2}{B^2}=1$$ given five points of the ellipse?
How to find an ellipse, given five points?
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conic-sections