Surface integral problem

[frigo303]

Hi,

I am looking to find the surface of the volume of f(x,y,z)->a=x^2+y^2-z^2 (a is a constant>0)

and the two curves
y=x/2-3
y=-x/2+3

I plotted the projection on the 2d plane here:




Any help and extra explanations are much appreciated!

 

[Deleted member 4993]

Hi,

I am looking to find the surface of the volume of f(x,y,z)->a=x^2+y^2-z^2 (a is a constant>0)

and the two curves
y=x/2-3
y=-x/2+3

I plotted the projection on the 2d plane here:


View attachment 16255

Any help and extra explanations are much appreciated!

What are the equations of those two curves?

 

[frigo303]

I rewrote this problem from memory from my test last week and completely missed the fact that I only gave the 2D projections of the curves... They are supposed to be planes. I think the equations weresomething along the lines of:

z=x/2-3+y
z=-x/2+3 +y

The graph is of the XZ plane by the way, X being the horizontal axis and Z the vertical.

 

[Cubist]

I don't think you are remembering the question correctly. Click the following link, or just type the equation into Google. It will show you a 3d graph of HALF of the surface formed by your equation "a=x^2+y^2-z^2"

z=sqrt(x^2+y^2-10)

it does not resemble your cross-sectional 2d graph

Also I don't think you have properly defined a surface. Was there a sketch with a region highlighted, or a limit on x,y,z or similar?

I recommend you wait for the teacher to return your papers. It can be a difficult wait ? hope you did well.