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Graphing a level surface f(x,y,x)=c 
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#1
Oct212, 03:31 PM

P: 128

1. The problem statement, all variables and given/known data
sketch the graph f(x,y,z)=x^{2} + (1/4)y^{2}  z, c=1 3. The attempt at a solution while i dont expect anyone to be able to graph it for me for i think obvious reasons, i have no idea how to interpret any of the information given to even attempt a graph. usually i would try to figure out how it looks in an 2d x,y plane and add the z dimension, but i cant do that with this. please help 


#2
Oct212, 03:36 PM

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P: 21,216




#3
Oct212, 03:44 PM

P: 128




#4
Oct212, 06:06 PM

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P: 21,216

Graphing a level surface f(x,y,x)=c
Have you spent any time sketching graphs of quadric surfaces?
The thing to do in this problem is to recognize what sorts of shapes you get in various planes, not axes. For example, plane z = 0 intersects the surface in an ellipse. In other words, the cross section of the surface in the xy plane is the ellipse x^2 + (1/4)y^2 = 1. In the plane z = 1, the cross section is the graph of the equation x^2 + (1/4)y^2 = 0, which is a degenerate ellipse that consists of only a single point. In other planes that are parallel to the xy plane, you get different ellipses. In the xz plane (where y = 0) what shape do you get? In the yz plane (where x = 0) what shape do you get? If you get a few cross sections at various places, you can start to get an idea of what the overall surface looks like. 


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