Finding angle of rotation of an ellipse

Question

Suppose I have the ellipse $$ x^2 -2xy +4y^2 = 1 $$

How can I find the angle at which this ellipse is rotated?

I have tried to assign $x=\cos\theta, y=0.5\sin\theta$ but I don't know if that's the way

Answer 1

Hint: look for the eigenvectors of \begin{pmatrix} 1 & -1 \\ -1 & 4 \end{pmatrix}