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.

So that's what this equation will look like.

And so this is a circle.

So you take all the multiples of v1, you're going to get every point along this line.

So I can get to any of these vectors.

Use push pull to push this surface inward.

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The conventional picture of the Big Bang is a point.

We'll be talking about it in Unit 6,

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So we could take this line right here, and add vector b to it.

But like all systems, it has a weakness.

Finally, there's a sixth path.

And you have a point, that's our focus, and it's the coordinate a comma b. that the locus of all points in the xy plane that are equidistant to this focus and this directrix has a shape that

And the answer is 7.

It's actually a fairly common picture.

The solution is to add the location to the x and y coordinates being generated.

To see take the equidistant line between C1 and C2, and you find that all data points are associated with C1 except for this one over here.

We are not going to see the image of the star and the planet as this.

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

So the line will look like this.

It moves in a gait that an insect uses, and here it is going on the treadmill.

But when it happens, be upset a little bit or be happy a little bit but keep it all in perspective.

So I have hopefully shown to you that the locus of all points that are equidistant to this point which is really just an arbitrary point.

As we showed in lecture, in order for there to be an Eulerian path every node in the network needs to have even degree, except for the starting and ending nodes, which are odd.

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I want to write this in scientific notation, so I take the leading digit, 1, put a decimal sign.

So you're going to get some vector.

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And further, the data points that belong to the same class

So I want to find all of the x, y's all of the points that satisfy an equation where their distance to the focus is equal to their distance to the directrix.

Doing so moves all the vertices by this amount.

And, actually, this is often used as the definition for an ellipse, where they say that the ellipse is the set of all points, or sometimes they'll use the word locus, which is kind of the graphical representation of the set of all points, that where the sum of the distances to each of these focuses is equal to a constant.

And we'll actually see soon that when you actually change this relation in this case, we found that all of the points that are equidistant to the focus and the directrix.

And we want to find all of the x and y's where the distance to the focus is equal to the distance to this

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If you were to stand at the North Pole, everywhere you looked, in all directions, would be south.

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In fact the locus of all points are the hyperbole in fact is all of the points that satisfy that condition.

So you can immediately see that this is not tracing out a line.

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