Answer
$B^2-4AC \lt 0$, and $A\ne C$
Work Step by Step
The general equation of a conic has the form of $Ax^2+Bxy+Cy^2+Dx+Ey+F=0(1)$
(a) When $B^2-4AC=0$, then a conic defines a parabola.
(b) When $B^2-4AC \lt 0$, then a conic defines an ellipse and $A\ne C$
(c) When $B^2-4AC \lt 0$, then a conic defines a circle and $A=C$
(d) When $B^2-4AC \gt 0$, then a conic defines a hyperbola.
The conic represents an Ellipse; thus we have: $B^2-4AC \lt 0$, and $A\ne C$