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Twin parabolas in three-dimensional space are two congruent parabolas lying in two perpendicular planes such that the vertex of the one is the focus of the other. This Demonstration shows that a cone with its apex at some point on one of the parabolas and with its axis tangent to the parabola at that point can be constructed (by choosing an adequate opening angle) so that it contains the other parabola. In fact, every point of one parabola can serve as the apex of some cone containing the other parabola, and there is no other possible cone apex with this property anywhere else.
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