Given $a>0$ and $ac-b^2>0$ show
$cy^2+a[(x+\frac{by}{a})^2-(\frac{by}{a})^2] > 0$
I'm completely confused about this, I've tried a few approaches. I end up getting stuck saying that I know $cy^2>0$ using the 2nd of the given inequalities, but I can't show the $a[...]$ part is >0 since all I know is x and y are non-zero.
Any guidance? Comes from a larger question about showing a symmetric matrix [a, b, b, c] is positive definite if that helps.
Thanks for any nudges :)