In my textbook I am told about a conic section with equation:
$$9x^2 -4y^2 -54x - 16y + 29 = 0$$
and it mentions in passing that since the $xy$ term is $0$ then the centre is:
$\frac{54}{2\times9}, \frac{16}{-2\times 4}$
Presumably they are implicitly using a rule that looks like:
$α = \frac{-D}{2A}, β=\frac{-E}{2C}$ where $(α,β)$ is the centre of a conic section with general form
$$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$$
But I've not come across a rule like that. So my question is firstly, am I even inferring the correct rule? And secondly, why does this work?