GeoGebra Classroom

# Exploring Conic Section Possibilities

## 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?

## 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?

## 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?