Ellipses can degenerate to two parallel lines: x^2+a^2y^2-1=0 or the double line x^2+a^2y^2-a^2=0, as a goes to 0; but, because they have conjugate complex points at infinity which become a double point on degeneration, cannot degenerate to two intersecting lines.
A double line cannot degenerate to the other types.