I’m studying conic sections, and this question had me stumped.
What restriction should be put on the constants so that the general equation for any conic section, $Ax^2+ Bxy+ Cy^2+ Dx + Ey +F =0$ will always represent a conic?
I’ve scoured the Internet but can’t find any webpage which has the answer to this question.
I thought of the restrictions $A≠0$ and $C≠0$, but I came across a degenerate conic (a line) in which $A=0$ and $C=0$. In this case, the restrictions $A≠0$ and $C≠0$ would no longer be suitable, unless a degenerate conic is not considered as a conic.
Or, if rotated conics are not considered as conics, then a suitable restriction would be $B=0$.
Are my assumptions correct?