Not being able to understand intersection of two cones.

Question

I do understand that when a plane cuts a cone it does in two lines, but where did the other two lines come from? The solution(see pic) says that "the two cones intersect in four lines", now how is that possible? It should have been two lines as a plane is cutting a cone(only one and not two).

Answer 1

Sometimes a picture is worth a thousand words: