Boundedness of a set Let $$S = \{(x, y) \in \mathbb{R}^2: x^2 + 2hxy + y^2 =1\}$$
For what values of $h$ is the set $S$ nonempty and bounded?
For $h = 0,$ it is surely bounded, the curve being the unit circle. What for other $h$?
Please help someone.

Hint:
$x^2+2hxy+y^2-1=0$ is a conic, and it is an ellipse if its discriminant $B^2-4AC=4(h^2-1)$ is negative.  
