Conic Sections: Introduction

Explore with this app for a bit. Then use it to help answer the thinking questions that follow.
1.
[color=#bf9000][b]Note the equation of the plane is z = some constant. [/b][/color][color=#bf9000][b]Change the equation of this yellow plane to z = 2. [br]Then change it to z = 1. [br]Then change it to z = 4. [/b] [/color][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]?
2.
Change the [color=#bf9000][b]equation of the plane[/b] [/color]to [math]z=x+2[/math] . How would you describe the intersection of this [color=#bf9000][b]plane[/b][/color] and [color=#1e84cc][b]double-napped cone[/b][/color] now?
3.
Change the [color=#bf9000][b]equation of the plane[/b] [/color]to [math]z=0.5x+2[/math] . How would you describe the intersection of this [color=#bf9000][b]plane[/b][/color] and [color=#1e84cc][b]double-napped cone[/b][/color] now?
4.
Change the [color=#bf9000][b]equation of the plane[/b] [/color]to [math]z=4x+2[/math] . How would you describe the intersection of this [color=#bf9000][b]plane[/b][/color] and [color=#1e84cc][b]double-napped cone[/b][/color] now?
Close
– Tim Brzezinski

Information: Conic Sections: Introduction