# Homework Help: Sketch the surface

1. Jan 15, 2010

### anubis01

1. The problem statement, all variables and given/known data
Sketch the surface x+y2+z2+1=0

2. Relevant equations

3. The attempt at a solution
I'm not to sure how to proceed with this. My initial idea was to re-arrange for x such that
x=-1-y2+z2=-1-r2

thus the equation for the surface becomes y2+z2=r2

I'm not sure what to do next though.

2. Jan 15, 2010

### benorin

$x=y^2+z^2$ is a bowl opening which direction?
$x=1+y^2+z^2$ is the same bowl shifted one unit in which direction?
$x=-(1+y^2+z^2)=-1-y^2-z^2$ is the second bowl reflected about which axis?

3. Jan 15, 2010

### anubis01

okay x=y2+z2 is a bowl opening in the x direction
x=1+y2+z2 is the same bowl shifted by 1 unit to the right along the x-axis

x=-1-y2-z2 is the same bowl reflected along the negative x-axis.

So the image should be a bowl that runs along the positive and negative x-axis.

4. Jan 15, 2010

### benorin

no picture? :(

5. Jan 15, 2010

### anubis01

heres the picture I drew, I wasn't quite sure whether to draw the two bowls as connected or seperated object

http://img62.imageshack.us/img62/465/cci1501201000000.jpg [Broken]

Last edited by a moderator: May 4, 2017
6. Jan 15, 2010

### benorin

$x=-(1+y^2+z^2)\le -1$ right?

7. Jan 15, 2010

### anubis01

ah, so then the bowl only runs along the negative x axis like this
http://img25.imageshack.us/img25/465/cci1501201000000.jpg [Broken]

Last edited by a moderator: May 4, 2017