So your distance between the two left and right points in a horizontal ellipse is the same as the distance between the two

As the crow flies ?

In the ellipse, you're taking the sum of the distances to the focus points and saying it's a constant.

Well, it's joules.

This light blue distance is the same, the distance from this vertex or from this leftmost point of this rightward opening hyperbola to this focus is the same as this distance.

You have this force times distance expression right here.

line right there.

Same thing, that's this line.

If you go straight, about 200 metres, but there's no going straight here.

Two km to cover in 10 minutes. Straight?

There will probably be this point right here because the distance from there to there is this name as the distance from if you just drop a line straight down.

And so if we were to graph this that's my y axis, that's my x axis and the focal length is the distance to, in this case, to the left and the right of the origin.

But it didn't start out that way.

This is our focus.

And words, it just means.

So it would be the distance around.

As we get really far away, the stars are predicted to move slowly again.

We could have said something like this distance, but this distance wouldn't be the shortest distance between this point and this line.

Distance

Distance exponent

At a distance of

Distance

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

And for all the other states, I've written in red the straight line distance.

In particular, each cluster center represents half of the space.

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.

These two focal lengths are symmetric.

On the graph paper, you can see how all the lines on the graph paper have been distorted.

The goal, again, is Bucharest, and so the distance from Bucharest to Bucharest is, of course, 0.

Slice distance

Distance Test

Angular Distance

Angular distance

But I have a strong feeling he'll be there. ( ominous theme playing ) How far is it?

2200 feet.

How much further?

How far?

Distance.

Distance.

curve

Curve

Curved

Well, it's just the difference in y because no matter where we are we're just going to drop down straight to the directrix.

A nice visual composition of symmetry.

So if this distance is the same as this distance, then the magenta distance minus this blue distance is going to be equal to this green distance.