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.

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 that's what this equation will look like.

Use push pull to push this surface inward.

This is all your fault.

We'll be talking about it in Unit 6,

I agreed with you in all your views.

Finally, there's a sixth path.

So I can get to any of these vectors.

And the answer is 7.

It all makes sense now.

The conventional picture of the Big Bang is a point.

Now, that is the India that is emerging into the 21st century.

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

He got 100 percent in all the important things,

And they are also going to work on targeted promotions.

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

There's one more useful thing we can add to our polygon creator, changing the radius of the polygon.

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

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

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.

But like all systems, it has a weakness.

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.

We should be conscious of our shortcomings.

You should perform regular maintenance on your car.

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

So essentially, this equation is the plot of all points that are exactly d away, a distance of d away, from the point 0,0, and that's just a circle.

The mission didn't work.

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 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.

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.

line for my circles. so a circle looks something like that.

It's actually a fairly common picture.

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

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.

But I think this collinearity of it makes more sense to you if you say, oh, let's draw them all in standard form.

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.

let's call this d1 nope, too thick let's call that d1, this is d2 that that's going to be equal to a constant number along the whole ellipse.

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

At this time, you don't need to understand everything.

You don't need to understand everything right now.

'What did they draw?' said Alice, quite forgetting her promise.

Say I can choose K to be 1, 3, 5, 7, or 9.

There is no reason to doubt that this would be a wrong claim based on the sample that we've drawn.