# Exploring Conic Section Possibilities

- Author:
- Tim Brzezinski

## STUDENTS:

In each of the apps below, a

**plane**intersects a**double napped cone**.## In the app above:

Note the equation of the plane is z = some constant.
Change the equation of this plane to .
Then change it to .
Then change it to .
How would you describe the intersection of this **plane **and **double-napped cone**?

## 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? How would you describe them?