# Homework Help: How do you find a level surface representing another surface?

1. Feb 1, 2012

### shalanheyyo

1. The problem statement, all variables and given/known data
The surface S is the graph of f(x,y) = sqrt(25-x^2)

a)Find a level surface g(x,y,z) = c Representing S.
b) with C=?

2. Relevant equations

3. The attempt at a solution
I have no idea what to do with this question. How should I find g(x,y,z)? Do I let sqrt(25-x^2) = C? I tried this method and the answer is wrong. Am I on the right track?And what does it mean by C=?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 1, 2012

### Simon Bridge

http://math.arizona.edu/~calc/Text/Section12.5.pdf [Broken]
... but surely you've covered this?

Don't know what it means by C=?
Does not look like a general notation.

Last edited by a moderator: May 5, 2017
3. Feb 1, 2012

### shalanheyyo

I missed 2 weeks of lectures because I was sick, so I am having a really difficult time to catch up...
So basically I take sqrt(25-x^2)-z and solve it for Z?

Last edited by a moderator: May 5, 2017
4. Feb 1, 2012

### Simon Bridge

Ah - then you should read through that link I gave you.
It is very hard to give you hints without doing the thing for you it's that basic - the link covers the concepts and has examples.

Basically, you put g(x,y,z) = z-f(x,y) = c which gives you a family of 3D surfaces... now, if c=0, you get a simplification that will tell you the basic shape of the surface in 3D.

5. Feb 1, 2012

### HallsofIvy

First, $f(x,y)= \sqrt{25- x^2}$ is not a surface in a xyz-coordinate system because you need a coordinate representing z. Rather $z= \sqrt{25- x^2}$ is a surface. And that is the same as $\sqrt{25- x^2}- z= 0$.

6. Feb 1, 2012

### Simon Bridge

I got my interpretation by googling for similar phrasing ... JIC.
shalanheyyo really needs to check with someone else on the course.

It could be the intent is that one put $z=f(x,y)$ then rearrange that so all the "constant" terms are on the RHS and all the terms with x or y or z in them are on the LHS. This would have form g(x,y,z)=c, and it would make sense to ask what c is.

7. Feb 1, 2012

### shalanheyyo

I emailed my Prof and the question is actually really simple. I guess I got confused by how the question is worded

8. Feb 1, 2012

### Simon Bridge

So are you going to enlighten us?