# Tangents to an ellipse

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!

• 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? Feb 28, 2013 at 16:12
• 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. Feb 28, 2013 at 16:12
• @Maesumi, correct: given a point P not on a conic, there are precisely two tangents from P to the conic (over $\mathbb C$). Feb 28, 2013 at 16:14
• 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. Feb 28, 2013 at 16:14
• I meant that the tangent line to specific conic intersects that conic at only one point on the conic. Feb 28, 2013 at 16:17