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Hello there.
00:01
So now we have the following equation 9xx squared minus y square plus 9 z squared minus 9 equals to 0.
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And we need to sketch the graph of this surface.
00:10
So the first thing that you should do is try to put this equation in a more familiar way.
00:15
So in this case, first i'm going to pass these 9 to the right hand side of the equation.
00:19
So we have the following 9x square minus y square plus 9 z squared equals to 9.
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And now you can see that this has more or less the structure of an hypervaloid.
00:33
You can obtain a better look of course if you divide by 9 the whole equation so you can have here a number one on the right hand side of the equation.
00:42
So then you obtain x squared minus y square over 9 plus z squared equals to 1 and this give you a most beautiful way to see the equation so you can infer which surface it's corresponds.
01:04
So, well, this is the equation of an hyperboloid because we have a number, a negative sign here in one of the variables.
01:12
So that implies that this will be an hyperboloid with the axis in the y direction.
01:19
And you can observe here that that is, this is the structure because, well, let's see, if you put y equals to zero, then you're working in the xz plane.
01:32
So, you're so it's a cross section in this part...