Now in the hyperbola, what is the difference of the distances to the two foci?

Now, we said that we have these two foci that are symmetric around the center of the ellipse.

So the entire time, the contents, the sum of the distances to the two foci was equal to 2a.

And in future videos I'll show you the foci of a hyperbola or the the foci of a well, it only has one focus of a parabola.

In the last video, we learned that an ellipse can be defined as the locus of all points where the sum of the distances to two special points, called foci and let me draw this all out, so that's my x axis the sum of the distance to these two special points, called focuses or foci, is a constant.

And we could use that information to actually figure out where the foci lie.

But the whole point of this video is to discuss foci, and you might have guessed and I did touch on it in the last video that hyperbola also have foci, but they open.

And then I have this distance over here, so I'm taking any point on that ellipse, or this particular point, and I'm measuring the distance to each of these two foci.

Now, the next thing, now that we've realized that, is how do we figure out where these foci stand.

They're going to be to the right and the left of these two points, so this is a let me do them in a bright color, because I want you see them let's say that those are the two foci and a hyperbola, this is and notice the difference.

We have two times two times two, times, two times two times two times two times two.

Two out. Two! Two!

Now the definition of a hyperbola, one of the definitions of a hyperbola, can be the locus of all points where you take the difference not the sum, you take the difference of the distances between the two foci, so if

Number Two. Number Two. Two.

And that's two times two times two times two times two.

Two times five is equal to two plus two plus two plus two plus two.

In fact this is equation of the hyperbola but instead set of writing b squared, since we wrote it, we essentially said, what is the locus of all points where the difference of the distances to those two foci is equal to 2a?

Two minutes, two minutes, two minutes.

Minus two, two?

Two times two.

Two minutes, two.

Two to the third is two times two times two, right?

Two times three is equal to two plus two plus two.

Well that's equal to two plus two plus two plus two.

Or we could've said two plus two plus two plus two plus two... twelve times.

What's two times two?

What's two times two?

Get two, get two.

Two minus two thirds

Two grand. Two grand!

Matrix A is a two by two, two rows and two columns.

One Two Three Four One Two Three Four Two Two Three Four

Two times seven is equal to well, I could write two plus two plus two plus two this is getting tiring plus two plus two.

One, two, three. One, two, three. One, two, three.

Jane Goodall Two, two, I'm going to take two.

I have one group of two, two groups of two, three groups of two, four groups of two.

Now we learned in the last video that one of the definitions of a hyperbola is the locus of all points, or the set of all points, where if I take the difference of the distances to the two foci, that difference will be a constant number.

An ellipse, one of the definitions of an ellipse, was the locus of all points or the set of all points where the distance from each of those points, the sum of the distance from each of those points to the two foci is a constant.

One times two is two.

Two plus zero is two.

Two equations and two unknowns.

So that's two plus two.

And what's two plus two?

Two hundred tomorrow. Two hun...

Two minus zero is two.