Given any second degree equation in $x$ and $y$,
is it possible to find out the centre and/or the axis of the conic section it represents?
What information can I gather simply by looking at the curve?
For example one thing my teacher taught me was that if $h=0$ the axis of the curve(be it parabola,hyperbola,ellipse etc) is parallel to the coordinate axes.
I am looking for some other information that the equation can offer.