Hi. Is there any way to know if a ellipse in the form $\displaystyle ax^2+by^2+cx+dy+e=0$ has a horizontal or vertical major axis without changing into standard form. For example, if I have the ellipse $\displaystyle 2x^2+3y^2-x+6y-2=0$ can I tell if it is horizontal or vertical without changing it into standard form. I would think that the quadratic term ($\displaystyle ax^2, by^2$) with the lower coefficent would be over $\displaystyle a^2$ , allowing one to determine whether it was horizontal or vertical, but I could be wrong. Could someone tell me if I am correct? Thanks!