00:01
We're asked to sketch and discuss this surface here, 4x squared plus y squared equals 16.
00:09
And so that's going to be an ellipse, basically extruded.
00:16
So it doesn't, there's no z dependence on this.
00:19
So if we make a contour plot, i basically use the contour plot.
00:26
I took this 4x squared plus y squared minus 16 and set that made a contour plot with a contour of c equals zero and so that basically what you see is you just get an elliptical tube um you can see here uh because again there's no z dependence on this i did i did it this way because you could say that this is um we could just say this is uh no that's not right so we could you know this is you know, it's just basically a implicit function of x and y, x, y, and z.
01:09
So we have to, we have to take a look at it as a, you know, as a function like that.
01:15
So if we plot, this isn't z equals this, right? we could think of this as a level set.
01:23
Again, we could either take this function here and then take the level set when x, or c equals 16, or then subtract x, subtract 16 and then take the level set.
01:33
We'll see you zero...