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

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In this model both curves have a tangent plane in common; the curve of intersection has one double point.

Circular cones are surfaces of the second order. If two surfaces of the second order intersect each other, generally an intersection curve of the fourth order is generated. This can have a maximum of one double point. If two double points occur, the curve collapses into two (flat) curves of the second order.