# Find the parameterization of a curve

1. Jan 4, 2014

### skrat

1. The problem statement, all variables and given/known data
Find a parameterization of a curve which we get from $x^2+y^2+z^2=4$ and $x^2+y^2=2x$.

2. Relevant equations

3. The attempt at a solution
I hope this doesn the job, I am just not sure, so if anybody could check my result I would be really happy.

I started with $x=1+\cos \vartheta$ for $\vartheta \in \left [ 0,2\pi \right ]$ and $y=\sin \vartheta$

Than from $x^2+y^2+z^2=4$, z as function of $\vartheta$ is $z=\sqrt{2(1-\cos \vartheta )}$

Or not?

Last edited: Jan 4, 2014
2. Jan 4, 2014

### BruceW

yeah, looks good to me. nice work there. you've chosen the positive root for z. so that gives one of two possible curves. There is another curve, but since they say just to find a parameterization of a curve, I guess you don't need to write down both curves.

3. Jan 4, 2014

Thank you!

4. Jan 4, 2014

### Ray Vickson

Please use correct punctuation: I first read your statement $x^2+y^2+z^2=4$ z as $x^2 + y^2 + z^2 = 4z ''$ (which is exactly how it is typeset) but it should be $x^2 + y^2 + z^2 = 4$, z ... .

5. Jan 4, 2014

### skrat

Thanks, I've edited the first post!