00:01
Let's find the distance between these two spheres.
00:04
The sphere x squared plus y squared plus z squared equals four, and x squared plus y squared plus z squared equals 4x plus 4y plus 4 z minus 11.
00:19
What's that distance going to look like? so let me do this as projections so i don't have a cluttered diagram.
00:28
Suppose that i have two spheres.
00:30
So here's one sphere and here.
00:34
Is another.
00:35
We're looking for this distance between them.
00:40
Well, that distance can be found by looking at the distance between the center of the two spheres minus the radius of each sphere.
00:59
And that will give us this distance in between that we are looking for.
01:05
So that's what we're going to do.
01:07
We're going to find the distances between the centers of each sphere.
01:12
And then subtract the radius of each sphere, and that will give us the distance between them.
01:21
Well, the first sphere has its center at the origin.
01:25
We don't need to do any work to see that, and we can see that its radius is two.
01:36
To find the center and radius of the second sphere, we're going to have to do some completing the square.
01:51
So let's rewrite our expression...