A problem I'm working on has the equation for a diagonal ellipse
$$5x^2 + 5y^2 - 6xy - 8 = 0$$
which can be rotated 45 degrees to get the vertical ellipse
$$\frac{x^2}{1}+\frac{y^2}{2^2} = 1$$
The problem is to find the eccentricity, directrices and foci of the diagonal ellipse, and I assume that since it made me perform this rotation, I'm supposed to utilize this new one.
I was able to find the eccentricity, directrices and foci of this vertical one, but I can't figure out how to use this to find the same attributes for the original, diagonal ellipse.