I know that for any nonzero $x,y\in\mathbf{R}$,
$ax^2+by^2+cxy > 0,$
where $a,b,c\in\mathbf{R}$. What can I deduce about $a$, $b$, and $c$?
For example, letting $x=1$ and $y=0$, I know that $\boxed{a>0}$. Letting $x=0$ and $y=1$, I know that $\boxed{b>0}$. Letting $x=y=1$, I know that $\boxed{c>-(a+b)}$.
What else can I deduce about $a$, $b$, and $c$? How will I know when it's time to stop looking? (Is that last question even answerable?)