The Geogebra 3D graphing tool will be a great support for the questions below:
- You are given the following cone and plane:
What shape is created by their intersection? Make sure you can prove your work. - You are given the following cone and plane:
What shape is created by their intersection? Make sure you can prove your work. - 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?
- 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. - 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.
Points of Discontinuity 