Degenerate conics are obtained when the slicing plane cuts the double right circular cone at the intersecting tips of the two cones (vertex). This gives a pair of straight lines intersecting at the vertex (depending upon the eccentricity). Dandelin spheres are useful in finding the focus, directrix, etc.
Focus of a straight line lies at infinity. I don't know what happens to the directrix of the conic when it approaches becoming degenerate. I think the Dandelin sphere gets smaller and smaller when the slicing plane moves towards the vertex of the two cones, but I am unable to explain this in relation to the focus and directrix.
So, what will happen to Dandelin Spheres, and their applications (finding focus, directrix, etc.,) in case of degenerate conics? Or is that not defined at all for such cases.