Tangents to an ellipse

Question

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!