Game of Cones

Geometry Level 2

You're operating a cone-cutting device with the high-energy laser beam. This laser ray is parallel to the sliding belt, and its generator is fixed at all time.

You may simply place a cone on its base or may tilt it a little with a machinery arm. However, if the cone is tilted over the angle \(\theta\) (within the cone), it will be toppled to the belt as shown in the picture.

Which conic section is visually impossible to achieve by this machine? (Assume that all the cones stay still enough to be cut.)

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