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

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In this model all the straight lines of the surface of one cone intersect the second one and one obtains two distinct space curves as intersection.

Right circular 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. The curve of the fourth order can have at most one double point. In case of two double points, the curve decomposed into two (plane) curves of the second order.