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A book I'm reading (Companion to Concrete Math Vol. I by Melzak) mentions, "...any ellipse occurs as a plane section of any given cone. This is not the case with hyperbolas: for a fixed cone only those hyperbolas whose asymptotes make a sufficiently small angle occur as plane sections."

It seems to me that all hyperbolic sections of the same cone must have asymptotes that make exactly the same angle with each other (the angle formed by two antipodal generators of the cone). Is this incorrect? The wording in the book suggests their angles fall a range of values.

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  • $\begingroup$ Perhaps you have a mental picture of orthogonal projection, when the projection is not always orthogonal? $\endgroup$
    – Charles Matthews
    Aug 16, 2012 at 11:30
  • $\begingroup$ This question would be more appropriate for other sites such as math.stackexchange.com; see the faq. MathOverflow is intended for research level questions. Voting to close. $\endgroup$
    – Lee Mosher
    Aug 16, 2012 at 13:43

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