Create any conic section with five points from an equation hiding in Pappus' theorem #SoME3

Conic sections are ubiquitous in math and unite many commonly studied curves such as ellipses, hyperbolas, and parabolas. However, interpolating points using conic sections is not that common, compared to using polynomials, for example. In this video, I derive an interpolated conic section equation using a seemingly unrelated theorem called Pappus' theorem. It is about a collection of points and lines from projective geometry that has a hidden and beautiful connection to conic sections. Desmos link of the interpolated conic section equation: https://www.desmos.com/calculator/onm... This video’s proof of Pappus’ theorem was inspired by the proof of Pappus’ theorem from this paper: https://arxiv.org/pdf/2011.12455.pdf Manim animations, voiceover, bgm: 206p