Warm-up Time
Today, we will be exploring Conic Sections. Conic Sections are the shapes made when a flat surface slices through a cone. Depending on how the cone is sliced, the shape can be a circle, ellipse, parabola, or hyperbola.
Click here to begin
Explore Coinc Sections
All right, dudes! Let's begin exploring Conic Sections by venturing into the three tabs below!Click on either the tab title, or the picture underneath the tab.
What is a Cone?
Defining Conic Sections
Exploreing Conic Sections
Once you have finished exploring all three tabs, type word DONE in Engageli and close out of this tab!
The Cone
A Cone is a three-dimensional geometric shape with a circular base and a point called the vertex at the top. The sides of the cone are curved, tapering smoothly from the base up to the vertex. The height of the cone is the perpendicular distance from the base to the vertex. A cone can be thought of as having two main parts, called nappes:
- A single nappe is just one half of a cone.
- A double nappe is formed when two nappes are stacked tip-to-tip.
Double Nappe
Click here first
Single Nappe
Click here second
Conic Sections
A Conic section is a two-dimensional shape that is formed when a flat plane intersects a cone. The type of conic section produced depends on the angle and position of the slice.
- Nappe: One half of a cone.
- Double nappe: The full cone with two nappes stacked tip-to-tip.
- Vertex: The point where the two nappes meet at the tip of the cone.
- Plane: The flat surface that intersects the cone to produce a conic section.
Circle – Created when the plane slices horizontally across a single nappe of the cone. The resulting shape is perfectly round, and all points on the circle are the same distance from the center.
Click here to see picture
Click here for audio
Click here to see picture
Ellipse – Formed when the plane slices through a single nappe at an angle that is not parallel to the side of the cone. The shape is oval, with two foci that define its geometry.
Click here for audio
Parabola – Occurs when the plane slices parallel to one side of a single nappe. The resulting curve is U-shaped, and it has a single axis of symmetry. Parabolas are used in satellite dishes, bridges, and roller coasters.
Click here to see picture
Click here for audio
Hyperbola – Formed when the plane slices through both nappes of a cone. This creates two separate curves that open away from each other. Hyperbolas have two foci and appear in situations like cooling towers, navigation paths, and orbits.
Click here to see picture
Click here for audio
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Conic Section Matching
“This is your chance to test what you’ve learned about conic sections. Drag each conic section picture and drop it on the description that matches it. Use the information from Tabs 1 and 2 to help you match them correctly.”
Warm-up Time Conic Sections
Yaw Owusu-Akyaw
Created on November 4, 2025
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Transcript
Warm-up Time
Today, we will be exploring Conic Sections. Conic Sections are the shapes made when a flat surface slices through a cone. Depending on how the cone is sliced, the shape can be a circle, ellipse, parabola, or hyperbola.
Click here to begin
Explore Coinc Sections
All right, dudes! Let's begin exploring Conic Sections by venturing into the three tabs below!Click on either the tab title, or the picture underneath the tab.
What is a Cone?
Defining Conic Sections
Exploreing Conic Sections
Once you have finished exploring all three tabs, type word DONE in Engageli and close out of this tab!
The Cone
A Cone is a three-dimensional geometric shape with a circular base and a point called the vertex at the top. The sides of the cone are curved, tapering smoothly from the base up to the vertex. The height of the cone is the perpendicular distance from the base to the vertex. A cone can be thought of as having two main parts, called nappes:
Double Nappe
Click here first
Single Nappe
Click here second
Conic Sections
A Conic section is a two-dimensional shape that is formed when a flat plane intersects a cone. The type of conic section produced depends on the angle and position of the slice.
Circle – Created when the plane slices horizontally across a single nappe of the cone. The resulting shape is perfectly round, and all points on the circle are the same distance from the center.
Click here to see picture
Click here for audio
Click here to see picture
Ellipse – Formed when the plane slices through a single nappe at an angle that is not parallel to the side of the cone. The shape is oval, with two foci that define its geometry.
Click here for audio
Parabola – Occurs when the plane slices parallel to one side of a single nappe. The resulting curve is U-shaped, and it has a single axis of symmetry. Parabolas are used in satellite dishes, bridges, and roller coasters.
Click here to see picture
Click here for audio
Hyperbola – Formed when the plane slices through both nappes of a cone. This creates two separate curves that open away from each other. Hyperbolas have two foci and appear in situations like cooling towers, navigation paths, and orbits.
Click here to see picture
Click here for audio
What is your vibe today?
Happy/chill
Sad/Worried
Stressed
Tired/ Cant Even
Conic Section Matching
“This is your chance to test what you’ve learned about conic sections. Drag each conic section picture and drop it on the description that matches it. Use the information from Tabs 1 and 2 to help you match them correctly.”