INSTRUCTOR: Describe the set of points in three-dimensional space that satisfies x squared plus, parentheses, z minus 2, close parentheses, squared equals 16 and graph the surface. I'm going to put more emphasis on describing what this is than graphing, because my graph is going to be rudimentary. All right. So to begin with, this is a sphere. We know that the equation for a sphere is x minus a, close parentheses, squared plus the quantity y minus b squared plus the quantity z minus c squared equals r squared.

And this is most definitely a sphere. However, you may notice that there was no y term in that equation, which means this is a circle in the xz plane. So I'm going to draw a three-dimensional axis. OK. Let's see. There's x, y, and a z.

And in my xz plane, I'll draw a circle. However, the center of that is the point 0.2. That's because of the x minus 2 and just the x squared that's there. And the radius of that circle is 4, because 4 squared is 16.

So this is a circle in the xz plane with a radius of 4. And because there's no restriction on the y value, that means that this is a cylinder. So it's parallel to the y-axis. And note that lack of restriction means that it actually continues. And like I said, this is a poor graph, but it continues going in the y direction as far as we'd like.

Now, another way to have said this is this is a cylinder that extends indefinitely in the y direction that's centered on the line with x equals 0 and z equals 2. That's another way to describe what this is.