The model shows the penetration of two right circular cones whereas one of them can be pulled out in order to show the curve of intersection clearly.

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In this model both cones have two tangency planes in common; the curve of intersection splits up into two ellipses.

Rotary cones are surfaces of the second order. If two surfaces of the second order intersect, an intersection curve of the fourth order is generally created. This can have a maximum of one double point. In case two double point exist, the curve decays into two (plane) curves of the second order.