I need to calculate this elipse:

$\displaystyle $c^2=4x_1^2+3x_2^2-2\sqrt2{x_1x_2}$$

1. c^{2}=1

2. c^{2}=4

I need to calculate direction and the length of large and small axis of the ellipse.

(hint: own vector and Eigenvalues)

Thanks for your help.