| 11. | I assume the intersection between them is a conic section.
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| 12. | Non-degenerate conic sections are always " smooth ".
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| 13. | The value of e controls what kind of conic section the orbit is.
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| 14. | However, any two conic sections are projectively equivalent.
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| 15. | Surprising that neither parabola nor conic section gives this.
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| 16. | :: : Try the conic sections paragraph in Projective geometry # description.
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| 17. | The standard examples are the nondegenerate projective conic sections.
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| 18. | The image plane concretely realizes the abstract cutting plane in the conic section model.
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| 19. | And determines the shape of the conic section.
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| 20. | See Conic section # Degenerate cases for details.
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