What I found so far is following equations General Quadratic Equation: $$AX^2+BXY+CY^2+DX+EY+F=0 $$
Semi-major/minor axis Equation: $$a, b = \frac{1}{B^2 - 4AC} \sqrt{2 \left(AE^2 + CD^2 - BDE + \left(B^2 - 4AC\right) F\right)\left((A + C) \pm \sqrt{(A - C)^2 + B^2}\right)} $$
Coordinates of the center: $$ x_\circ = \frac{2CD - BE}{B^2 - 4AC} $$ $$ y_\circ = \frac{2AE - BD}{B^2 - 4AC} $$
Angle of rotation: $$\Theta = \begin{cases} \arctan\left(\frac{1}{B}\left(C - A - \sqrt{(A - C)^2 + B^2}\right)\right) & \text{for } B \ne 0 \\ 0 & \text{for } B = 0,\ A < C \\ 90^\circ = \frac{\pi}{2}^c & \text{for } B = 0,\ A > C \\ \end{cases}$$
But where can I find a resource (best would be a book) of this formulas? Is there a book with these general quadratic equations for ellipses?