Conical

Why on earth are they called conic sections?

Cone

Conical

Conic Sweep

(Louder cheer)

Can you give me the definition of a cone?

So let me see if I can draw a three dimensional cone.

Polyconic

The Japanese pride themselves on Mt. Fuji, a cone shaped mountain.

That's the beauty of democracy.

Now the intersection of this plane, which is now not orthogonal or it's not perpendicular to the axis of this three dimensional cone.

Let's see if we can learn a thing or two about conic sections.

(Laughter)

A small clay column was used for one, a clay ball was used for ten, and a large cone stood for sixty.

Circular

Now that you know what the conic sections are and why they're called conic sections, let's see if we can understand the actual equations of the conic sections a little bit better, and use that knowledge to be able to at least recognize them when we see the equation, and then if we see the equation, know how to plot them.

This one has four times the area, twice the diameter, but otherwise the same shape.

So this is a bit of a conundrum.

The same properties. The same viscosity.

So the first thing to recognize is that this is a hyperbola and we'll in a few videos, do a bunch of problems where the first point is just to identify what type of conic section we have and then the second step is actually graph the conic section.

Circular.

There you go.

And I even know a little bit about ellipses and hyperbolas.

And that's frankly where the word conic comes from.

Maybe I can find some kind of neat 3D application that can do it better than I can do it.

And at some point, the ellipse keeps getting more and more skewed like that.

Makes an elliptical or circular selection

If we said twice as far we would get another conic section.

Circular Arrow

A circular arrow

And you might wonder why I put it in this form.

I'm drawing it in such a way that it only intersects this bottom cone and the surface of the plane is parallel to the side of this top cone.

And then up here would be the intersection of the plane and the top one.

Remember, this plane goes off in every direction infinitely.

Let's see if we can learn a thing or two about the hyperbola.

So just as a review, I want to do this just so you see the similarity in the formulas or the standard form of the different conic sections.

in a circular region

Geometric Maltese Cross

Geometric Curved Four Point Star

Geometric Quarter Circle

Geometric Perfect Circle

You can almost view that I'm pivoting around this point, at the intersection of this point and the plane and the cone.

And then you would have something like this.

The first one I did was in the late 70's, and I just had a simple cone with a spigot at the bottom of it.