Given an arbitrary conic section in the form $$Ax^2 + Bxy + Cy^2 + Dx + Ey +F=0$$ (Where the coefficients are real valued) is there a simple test which can determine whether or not a particular conic is an ellipse? I know that if a conic section is an ellipse, then $A$ and $C$ will have the same sign, however I am not sure if this is a sufficient condition as well.
Edit: Forgot to include the "$...+F=0$".