For the following linear second order PDEs, the task is to identify in what regions of the two-dimensional plane the equation is elliptic, hyperbolic, or parabolic.
$$\sin(xy) u_{xx}\ -6 u_{xy}\ +u_{yy}\ =0$$
I began by composing the discriminant $\Delta^2 = B^2 -4AC$
$-1 \le \sin(xy) \le 1$
$32 \le 36-4\sin(xy) \le 40$
Then it is hyperbolic in the whole domain. Is that correct? And how I can sketch that in two dimensions?