I'm writing a paper on conic sections for my math research class in high school, and I was wondering if any of you know any challenging/interesting topics I can include in my paper regarding conic sections. I already have the basics i.e. proofs describing eccentricity and foci, but what else should I include? Below, I'm going to post some links to some questions regarding conic sections I found on Math.SE, and I would really appreciate it if I can get some of your opinions on whether or not I should include those topics. Thanks!
Usefulness of Conic Sections http://www.fen.bilkent.edu.tr/~franz/publ/conics.pdf The intersection of two conics - matrix solution CONICS, computing intersections, passing to complex numbers Visualizing the flat complex conic Rank of a degenerate conic Solving a Conic Matrix given these Equations Show that the rational conic $F(x,y)=ax^2+bxy+cy^2+dx+ey+f$, subject to a certain condition, is non-singular