00:01
In your question, it says sketch and given equation describing all points in 3d that are at a distance of 3 from this given equation of a sphere.
00:13
So what we need to understand here is basically the center coordinates are given in this format here.
00:27
So the x coordinate is 3 because it's always x minus the x coordinate.
00:33
Same for the y minus the y coordinate because this is a plus that means the coordinate must have been negative and then z does not have a plus or minus with it that means the z coordinate is zero another thing to pay attention to is that the radius of the given equation is found here but we have to think of we have to take the square root of that number because this part of the equation is supposed to be r squared so the r must have been a three so that when it's squared, it equals that nine.
01:08
So your current radius, current sphere is three.
01:12
So if we're going to make a new equation that shows all points that are three, a distance of three away from this sphere, we're basically creating a sphere that surrounds the original sphere.
01:29
Those are called concentric spheres, and we would just increase our radius by three.
01:38
So the new sphere is going to have the same coordinates for the center, making that part of the equation the same.
01:56
But our radius is now going to be three larger.
01:59
So new radius is going to be six.
02:05
And then when we six, we put six squared into the problem, that is going to be, because we have to square a radius, that is going to be 36.
02:16
Now your question says give an equation.
02:20
There would actually be another point that is the exact distance of three from all the points on the sphere.
02:29
And that would have been the center of the original shape.
02:34
So it is possible to write a second.
02:36
Second equation here, this equation is only going to describe one point, and i'm going to make its radius zero.
02:49
That basically means it's only the point at the center of the original sphere.
02:55
That point also would be a distance of three away from every point on the sphere.
03:01
But your question did say an equation like one singular, so they're probably only looking for this one, and that should be the equation part of your problem...