Change the parameters and manipulate the Cone View and Graph View to
find the different conic sections. As you explore, try to answer these
questions:
- How many different conic sections are there?
- How do the different conic sections look different in the Cone View? in the Graph View?
- What range or values do the parameters have for each conic section?
- What are the key features of each conic section?
- Can you create two identical Cone Views with different sets of
parameters? Is there a relationship in the parameters for these two
views? Do the Graph Views also look the same?
- When the cross section is an X, a line, or a point, it is
called a "degenerate" case because the graphs are not unique to conic
sections. Can you create these graphs? What are the parameters to create
them?
Here are some suggested parameters to guide your exploration:
Height | Slant | m | b |
1 | 0.5 | 1 | 1 |
1.5 | 0.5 | 1 | 1 |
1.5 | 0.5 | 0.5 | 1 |
1 | 1 | 0.5 | 1 |
1.5 | 1 | 0.5 | 1 |
2 | 1 | 0.5 | 1 |
2 | 1 | 0.5 | 0.5 |
1 | 1 | 0.5 | 0.5 |
1 | 1 | 0.1 | 0.5 |
1 | 1 | 0 | 0.5 |