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I want to plot the equation $x^2+y^2=z$ inside a volume. However I don't want to plot the center of the graph on the origin. "inspired" by the equation of a circle I tried: $(x-2)^2+(y-2)^2$ with hope of plotting the lowest point of the graph on the point $(2,2,0)$. I then tried $x+y=z$ and $(x-2)+(y-2)=z$ but this only affected it by $4$ on the $x$ axis, because it simplifies to $x+y-4=z$. (though I don't understand why this affects the $x$ axis and not the $y$ or the $z$ axi?)

How can I translate either Of those equations?

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1 Answer 1

So there are a couple of things going on here. Firstly, you are correct in one sense. $x^2 + y^2 + z^2= 4$ is the equation for a sphere centered around the origin in 3-space. $(x-2)^2 + (y-2)^2 + z^2 = 4$ is that same sphere, but with the center at $(2,2,0)$. So there, you are correct.

But in your second, $x + y - 4 = z$ or rather $x + y - z = 4$, these are planes in 3-space. The four offsets all three, x, y, and z coordinates (not just x). For example, one can see where the plane intercepts the three axes. In the case without the 4, all intercepts are at 0. But now, the x intercept is 4, the y intercept is 4, and the z intercept is -4. You might think - that's really weird! But a plane is rigid, and moving the x part affects the y part too.

Does that all make sense?

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@mixedmaths, Thanks for your answer, are you saying that 3d plots can only be translated in a a diagonal line, where the intercepts are all the same value? When I plot (x-2)+(y-2) it does only affect the x axis, see here on wolframalpha not affecting all three axis. Am I just looking at it wrong or something? –  Jonathan. Sep 5 '11 at 8:31
    
And I now tried a different graphing application and the same equation as in wolfram alpha I get different results? –  Jonathan. Sep 5 '11 at 8:49
    
@Jonathan: All graphing software that gives correct results will give the same results. When I plotted it on W|A, I noted that all axes were affected. I advise you to pay closer attention to the labelling of the axes, perhaps shift one variable at a time to see the difference. –  mixedmath Sep 5 '11 at 14:33
    
@mixedmaths, sorry wrong link wolframalpha.com/input/… –  Jonathan. Sep 5 '11 at 14:37
    
@Jonathan: I don't know why you think there is no difference. In the unchanged one, note that the plane intercepts the y axis at 0. In the second, it is not. The y shifts too. –  mixedmath Sep 5 '11 at 14:51

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