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

#### Raidan

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)

#### Ackbeet

MHF Hall of Honor
Try taking sections of it. If you plug in different values of $$\displaystyle z$$, what do you get in the $$\displaystyle xy$$ plane? Are there values of $$\displaystyle z$$ that are not allowed?

#### 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)

#### 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: #### 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)