So You Said Conic Sections Come From Slicing a Cone….?

  1. You are given the following cone and plane:Conics ResearchWhat shape is created by their intersection? Make sure you can prove your work.
  2. You are given the following cone and plane:Conics Research 3.pngWhat shape is created by their intersection? Make sure you can prove your work.
  3. Given a circular cone, the work to prove problems one and two is quite straight forward, but what shape is created by the intersection of the cone and plane below?Conics Research 2.png
  4. Taking a different perspective makes the answer to number two a bit more obvious, but just because something looks true does not mean it is:Screen Shot 2019-06-20 at 12.28.16 PM.pngTake a look at this video from Grant Sanderson and pause when he suggests you pause to give yourself a chance to come up with your own ideas. Once the video is complete, try to generate this proof for yourself.
  5. Are the proofs for why problem one makes a circle and problem two makes a hyperbola similar? Investigate by creating your own constructions and/or researching the work of others. In the end, generate your own proofs and be ready to explain to an audience.