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

The Geogebra 3D graphing tool will be a great support for the questions below:

1. You are given the following cone and plane:What shape is created by their intersection? Make sure you can prove your work.
2. You are given the following cone and plane:What 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?
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:Take 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.