When I was in Algebra 2, I remember that conic sections were really hard for me to visualize. The concept is a bit difficult to picture, so I have created this Instructable to help others who are also having difficulty understanding them. We are going to start with some background knowledge on what a conic section is and how they are produced, and then dive right into how we can make them using Tinkercad Codeblocks. This project is intended for students to make and understand but it can also be used for teachers to 3d print and use in class. All you will need for this project is a Tinkercad account, which you can create for free! The video above can be used to follow along with the written instructions, but I don't recommend using it by itself as I left helpful tips and notes throughout the written instructions. Let's get started!

*Credit to Lumen Learning for two conic section diagrams used in this Instructable

## Step 1: Background Knowledge

So what is a conic section? A conic section is a shape formed at the intersection of a double right cone and a plane. A double right cone is shown in Image 1. There are four main types of conic sections: circles, ellipses, parabolas, and hyperbolas. They are each shown in Image 2. There are a few more special cases of conic sections that are not as common as the four main types, but I will include them at the end of this Instructable as an extension for interested learners. Let's get started with the Tinkercad Codeblocks.

## Step 2: Set Up Your Project

1. Go to Tinkercad, and make sure you are logged in. (If you don't have an account you can make one for free!)

2. On the left hand column, click on Codeblocks.

3. Click on the blue button that says "Create New Codeblock", and then click "New Design".

4. On the top left, you should see a title to the right of the Codeblocks sign. Click on it to change it to whatever title you want. For the sake of this project, I will title mine Conic Sections Demo.

Your project is now set up and should look like the image above.

## Step 3: Make the Double Right Cone

Now we are going to make the double right cone, which we will use for the start of every conic section.

1. Drag a cone from the Shapes column onto the workspace.

2. Go to the Modify column and drag a move block underneath the cone.

3. Change the "z" to 10 so that the cone can be brought to ground level.

4. Repeat steps 1-3 one more time so that the process repeats twice.

5. Insert a rotate block from the Modify column and place it underneath the second move block.

6. Change the rotate block to rotate around Axis-y by 180 degrees.

7. Go to the Math column and insert an "X: Y: Z: " block into the space after pivot on the rotate block; change the "z" to 20.

Click on the play button at the top (to the right of speed) and see if your code makes a double right cone. After that, your screen should look like the image above.

*TIP: we will be using the code for the double right cone for each conic section so it is helpful to create multiple copies of it.

## Step 4: Make a Circle!

Now we will make a circle, the first of the four conic sections.

1. Go to the Modify column and drag a "Create New Object" block onto the workspace.

2. Click on the object name, select "Rename Variable", and call it Circle.

3. Insert the code for the double right cone underneath the Create New Object Block.

4. Drag a box from the Shapes column, and then select the gray circle with slanted stripes to make the box a hole instead of solid.

5. Drag a move block underneath the box and change the "z" to 45.

6. Go to the Modify column and drag a "Create Group" block under the move block.

7. Go to the Control column and drag a "Pause" block under the "Create Group" block.*

8. Go to the Modify column and drag a "Delete Object" block under the Pause block.

9. Go to the Data column and drag "Circle" into the space for Delete Object.

*NOTE: the pause block stops the code until you press play. The purpose for this is to stop the code so that you can examine the conic section created, and then once you understand it you can press play to move on to the next one.

Click on the play button at the top (to the right of speed), go to the top view of the workplane, and see if your code makes a circle. After that, your screen should look like the image above.

## Step 5: Make an Ellipse!

Now we are going to make an ellipse, the second conic section.

1. Create a new object from the Modify column and rename it to "Ellipse".

2. Insert the code for the double right cone underneath it.

3. Drag a box underneath the double right cone code and make it a hole instead of solid.

4. Click on the arrow on the right of the box block and change the dimensions to 25x25x25.

5. Drag a move block underneath it and change the "z" to 45.

6. Insert a rotate block from the Modify column and change it to rotate around Axis-y by 30 degrees.

7. Go to the Math column and insert an "X: Y: Z: " block into the space after Pivot; make the "z" 45.

8. Insert a "Create Group" block underneath the rotate block, and then a Pause block after that.

9. Drag a "Delete Object" block from the Modify column and then drag "Ellipse" into the space from the data column.

Click on the play button and then click it one more time when it stops at the circle so that you can see the code for the ellipse in action. Then go to the top right view of the workplane, and see if your code makes an ellipse. Your screen should look like the image above.

## Step 6: Make a Parabola!

Now we are going to make a parabola, the third conic section. This one is a bit harder to see, but it helps to look for a U-shaped curve.

1. Create a new object and rename it "Parabola".

2. Insert the code for the double right cone underneath it.

3. Insert a box underneath it, make it a hole, and click on the arrow to the right to change the dimensions to 25x25x25.

4. Drag a move block underneath it and change the "x" to 10 and the "z" to 45.

5. Insert a rotate block from the Modify column and change it to rotate around Axis-y by 60 degrees.

6. Go to the Math column and insert an "X: Y: Z: " block into the space after Pivot; make the "x" 10 and the "z" 45.

7. Insert a "Create Group" block underneath the rotate block, and then a Pause block after that.

8. Drag a "Delete Object" block from the Modify column and then drag "Parabola" into the space from the data column.

Click on the play button and then click it again every time it pauses so that you can see the code for the parabola in action. Then go to the right view of the workplane, and see if your code makes a parabola. Your screen should look like the image above.

## Step 7: Make a Hyperbola!

Now we are going to make a hyperbola, the last main conic section. This one is also a bit hard to see, but it helps to look for two U-shaped curves that are symmetric about where the two cones intersect.

1. Create a new object and rename it "Hyperbola".

2. Insert the code for the double right cone underneath it.

3. Insert a box underneath it, make it a hole, and click on the arrow to the right to change the dimensions to 20x20x50.

4. Drag a move block underneath it and change the "x" to 15 and the "z" to 20.

5. Insert a "Create Group" block underneath the move block, and then a Pause block after that.

6. Drag a "Delete Object" block from the Modify column and then drag "Hyperbola" into the space from the data column.

Click on the play button and then click it again every time it pauses so that you can see the code for the hyperbola in action. Then go to the right view of the workplane, and see if your code makes a hyperbola. Your screen should look like the image above.

Now you are done with the four main conic sections! The next part of this Instructable is an optional extension that goes over two special cases of conic sections.

## Step 8: Extension Background Knowledge

There are a couple special cases of conic sections in addition to the four main types. The two that we will be going over in this Instructable are the point and the degenerate hyperbola. The point is formed by a plane slicing through where the two cones meet, as shown in Image 1. The degenerate hyperbola, also called intersecting lines, is formed when a hyperbola goes through the center of the cones, as shown in Image 2. Now let's make these special conics using Tinkercad Codeblocks.

## Step 9: Extension: Make a Point!

Now we are going to make the point.

1. Create a new object and rename it "Point".

2. Insert the code for the double right cone underneath it.

3. Insert a box underneath it, and make it a hole.

4. Drag a move block underneath it and change the "z" to 30.

5. Insert a "Create Group" block underneath the move block, and then a Pause block after that.

6. Drag a "Delete Object" block from the Modify column and then drag "Point" into the space from the data column.

Click on the play button and then click it again every time it pauses so that you can see the code for the point in action. Then go to the top view of the workplane, and see if your code makes a point. It is a bit hard to see but you should be able to see that the cone forms a point at the top. Your screen should look like the image above.

## Step 10: Extension: Make a Degenerate Hyperbola!

Finally, we will make a degenerate hyperbola.

1. Create a new object and rename it "Degenerate Hyperbola".

2. Insert the code for the double right cone underneath it.

3. Insert a box underneath it, make it a hole, and click on the arrow to the right to change the dimensions to 20x20x50.

4. Drag a move block underneath it and change the "x" to 10 and the "z" to 20.

5. Insert a "Create Group" block underneath the move block, and then a Pause block after that.

6. Drag a "Delete Object" block from the Modify column and then drag "Degenerate Hyperbola" into the space from the data column.

Click on the play button and then click it again every time it pauses so that you can see the code for the degenerate hyperbola in action. Then go to the right view of the workplane, and see if your code makes a hyperbola. Your screen should look like the image above.

## Step 11: Assess Yourself

You are done! You just finished making the four main conic sections and two special conic sections. If you learned everything correctly, you should be able to take this quiz to assess yourself:

1. What is the name of the figure that planes intersect to form conic sections?

2. What are the four main conic sections?

3. Which conic section results in a U-shaped curve?

4. Which conic section can be represented by a football?

5. What is the name of the conic section that results in intersecting lines?

BONUS: How is the formation of a circle different from an ellipse in terms of the plane that intersects the double right cone? How is the formation of a parabola different from a hyperbola in terms of the plane that intersects the double right cone?

1. A double right cone

2. Circles, ellipses, parabolas, and hyperbolas

3. A parabola

4. An ellipse

5. A degenerate hyperbola

BONUS: The plane to form a circle is horizontal while the plane to form an ellipse is angled. The plane to form a parabola is also angled, while the plane to form a hyperbola is vertical.

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