Kevin Yang

⌛ Conic Sections

Second PSET of the year!

Conics have always been a subject of fasciation for me and finally learning them in a classroom setting is a real treat! Just the sheer idea that 3 completely different graphs, parabolas, ellipses, and hyperbolas, can be related to each other through two cones and a slicing plane is mind boggling! The diagram is so simplistic, yet the shapes that come of it are so complex! Elegancy 💯!

Note: For challenge problem 5, I wrote it out on paper as the majority of it was graphing (and LaTex graphing is not fun in the slightest). My approach can be summarized as implicitly differentiating to get the slope of the tangent line of the parabola, and then showing through geometry + difference of tangents that the incoming angle of a ray is equal to the out going ray + the bounce caused by the tangent line, which equals the angle between the focus and the bounce point, thus showing that all incoming rays will bounce to the focus.

My Responses:🔗

Original PSET:🔗

Note: The problems of this PSET are not mine, they are my math teacher, Ryan Normandin's. All rights are reserved to him, reproductions of this PSET are forbidden.