So this is the distance to the focus.

The minimum distance between Sebatik Island and the mainland of Borneo is about .

The distance from the center to a focus is formula_15.

So what's the distance between x, y and the focus?

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.

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

And we learned that the focus, the focal distance or the distance from the central of the ellipse, which is this distance right here that focal distance is just the square root of the difference of these two numbers.

So the distance to the focus is going to be equal to d sub 2.

And if I were to measure the distance from this point to this focus, let's call that point d3, and then measure the distance from this point to that focus let's call that point d4. d4.

For all of the points in the xy plane that satisfy the conditions that its distance to the focus is equal to the distance to this line.

And then you know the distance from the vertex to the focus, and you know the distance from the vertex to the directrix, and you're all done.

So here we set up the equation for all of the x's and y's where the distance to the focus is equal to the distance to 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.

So it would be that distance plus that distance plus that distance plus that distance.

This distance is the same distance as this distance right there.

And the actually equation, we actually just took an arbitrary xy in the coordinate plane, and we said that xy has to satisfy the condition that its distance to this focus is equal to that this distance right here is equal to this distance here.

This distance is the distance squared.

From that distance to that distance.

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.

This distance squared plus this distance squared is going to equal that distance squared.

Distance

Distance

Distance

Distance

Distance

That this distance is equal to this distance

This magenta distance minus this light blue distance.

Minimum

Minimum

Minimum

Minimum

Minimum

Minimum

Minimum

Minimum

So that distance is the same as that distance.

We're measuring a distance a distance to go around.

This distance right here is 3, this distance right here is 3, this distance right here is 2, this distance right here is 2.

And so if this is at distance 0, we could call this distance out here distance d.

If this is one focus point right here, and this is the other focus point, this ellipse could be defined as the set of all points, or the locus of all points, where if I take the distance of any one of these points that exist on the ellipse and take the distance to each of the locuses sorry, each of the focuses if I take that nope, I don't want to do that if I take that distance and add it to this distance, so

Subject Distance

Subject Distance

Maximum distance

Fade distance

Slice distance