Exploring Conic Section Possibilities

STUDENTS:
In each of the apps below, a [color=#bf9000][b]plane [/b][/color]intersects a [b][color=#1e84cc]double napped cone[/color][/b].
In the app above:
Note the equation of the plane is z = some constant. [br][br]Change the equation of this plane to [math]z=2[/math]. [br]Then change it to [math]z=1[/math]. [br]Then change it to [math]z=4[/math]. [br][br]How would you describe the intersection of this [b][color=#bf9000]plane[/color] [/b]and [color=#1e84cc][b]double-napped cone[/b][/color]?
In the app below, use the tools of GeoGebra to prove your assertion is correct.
Change the equation in the app below to create an entirely different cross section.
How would you describe this cross section in your own words? What does it look like?
Can you create an another cross section that's different from the other 2 examples above? Try to do so.
How would you describe this cross section in your own words? What does it look like?
Can you create a cross section different from the other three? Try to do so!
How would you describe this cross section in your own words? What does it look like?
Is it possible to create a cross section that is not curvy? How could we do it here?
What do you think?
When a plane intersects a double-napped circular cone, what could possible cross sections look like? [br]How would you describe them?
Close
– Tim Brzezinski

Information: Exploring Conic Section Possibilities