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).

Presumably these cones are not required to be circular cones, and then four lines of intersection are quite possible. In plane geometry, a circle and an ellipse can intersect in four points. Now in three dimensions, you can build cones on such a circle and ellipse, with the same vertex for both cones. These cones intersect in four lines, the lines joining the vertex to the four intersection points of the circle and the ellipse. — Andreas Blass, Apr 10 '20 at 18:39

score 1 · Accepted Answer · answered Apr 10 '20 at 18:37

1

Sometimes a picture is worth a thousand words:

answered Apr 10 '20 at 18:37

David G. Stork

29,774

Not being able to understand intersection of two cones.

1 Answers1