Parabola.

It looks like a parabola.

I know what a parabola is.

Well, the only other part of the hyperbola that we might be able to work something out is this part of the hyperbola right over here.

A parabola looks something like this, kind of a U shape and you know, the classic parabola.

And that's the parabola.

And this was a company where I built parabolas,

And this was a company where I built parabolas, I took metal shop, and I remember walking into metal shop building parabolas and Stirling engines.

That parabola looks something like this.

Now we can graph our parabola.

We put it in the equivalent of splints.

Let me draw that parabola right there.

So this is the vertex of this parabola.

And then the graph of this parabola is going to look something like this.

And there you get your parabola.

Your parabola is going to look like that.

We care about where it intersects the parabola.

Parabola is what happens when one side of an ellipse pops open and you get this parabola.

That's the two 0's of this parabola.

But this is a general form of a parabola.

So let's say I have a parabola y minus

I give you the parabola y minus y1.

And so the graph of that parabola will look something like this.

They're the circle, the ellipse, the parabola, and the hyperbola.

line and the parabola, is minus x0 minus 1 over 2 x0.

So the vertex of this parabola I'll just do a quick graph right here the vertex of this parabola occurs at the point 4, 21.

And they're saying that a normal line is something, when the first quadrant intersection with the parabola is normal to the parabola.

Where it's just a particular point on the parabola.

It's going to be a downward slope, downward opening parabola.

So this is at plus 3 comma 0. The hyperbola will open up like that.

They're telling us that this parabola, the shape of the parabola, can be represented or even better, they're saying that the cable that connects these two is in the shape of a parabola.

Or something pretty similar to what we know as a parabola.

So, x is equal to negative 3 4 is the vertex of this parabola.

So we have the left half of a parabola right here.

So the hyperbola is going to look like this.

What is that focus and that directrix for this particular parabola?

It's kind of the classic U shaped parabola that

So once again, we had the parabola y minus y1 is equal to

Or you could just recognize this is the vertex of the parabola.

So you're at the same point in the parabola.

So the intersection of our normal line and our parabola is equal to this.

Let us define a normal line as a line whose first quadrant intersection with the parabola is perpendicular to the parabola.

So if you're given this parabola, or if you can get a parabola to this form, how do you figure out the a's, the b's, and the k's so you know the coordinates of the directrix and the focus?

But I just want to figure out the 0's of this parabola first.

So that right there is the highest point of our parabola.