# x^2+y^2+z=1 sketch

• June 7th 2010, 08:54 AM
Raidan
x^2+y^2+z=1 sketch
Hi,
I'm having difficulty with this eqatuion and wanted to know what is this equation? is it a cone? and how would i sketch the points...Thank you for your time..(Hi)
• June 7th 2010, 09:00 AM
Ackbeet
Try taking sections of it. If you plug in different values of $z$, what do you get in the $xy$ plane? Are there values of $z$ that are not allowed?
• June 7th 2010, 09:05 AM
Raidan
Its actually to verify stokes theorem...x^2+y^2+z-1=0 where z is equal to or larger than 0...I just wanted to know how to sketch it and how to go about it. Thank you!(Smirk)
• June 7th 2010, 11:27 AM
p0oint
x^2+y^2+z-1=0

Now x^2+y^2-1=-z

and z=1-(x^2+y^2)

Do you know what is z1=x^2+y^2. It is paraboloid.

Its sections x^2+y^2=k or x^2+y^2=Sqrt[k]^2 are circles with radius Sqrt[k].

So first draw the paraboloid. Then reflect it around the z-axis (just turn it upside down), and finally move it for 1 unit up in the z-axis.

Regards.

P.S The graph that you need will look something like this:

http://lh3.ggpht.com/GraphicsRunner/...araboloid5.jpg
• June 8th 2010, 04:39 AM
Raidan
I see..thank you for making it clearer..I also have a question regarding the polar co-ordinates for a paraboloid and its boundary conditions..and also..how to convert them for the stokes theorem..Thank you!! (Rofl)