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I was reading a section on conic sections in a book, and the author writes proofs that show that tangent lines to each of the three non-degenerate types of conic sections intersect at only one point. What's the point of doing this? I'm writing a math research paper for high school, and I'm unsure as to whether to include his proofs or not. Any response will be appreciated, thanks!

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  • $\begingroup$ Looks to me as if your statement is insufficiently quantified, so that for the life of me, I can’t figure out what was being claimed. Could you quote one of these statements exactly? $\endgroup$
    – Lubin
    Feb 28, 2013 at 16:12
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    $\begingroup$ What do you mean "intersect at only one point"? The statement is not clear. Obviously the tangent lines to a circle do not intersect at one one point. $\endgroup$
    – Maesumi
    Feb 28, 2013 at 16:12
  • $\begingroup$ @Maesumi, correct: given a point P not on a conic, there are precisely two tangents from P to the conic (over $\mathbb C$). $\endgroup$
    – Lubin
    Feb 28, 2013 at 16:14
  • $\begingroup$ I'm going to the library this afternoon to find the book again, so hopefully I will be able to give you a quote. If it helps, he was using vectors and the property that sum of the distances from one point on the ellipse to the two foci is constant for any point on the ellipse. $\endgroup$
    – joejacobz
    Feb 28, 2013 at 16:14
  • $\begingroup$ I meant that the tangent line to specific conic intersects that conic at only one point on the conic. $\endgroup$
    – joejacobz
    Feb 28, 2013 at 16:17

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