# Convert ellipsoid from cartesian to spherical equation

1. Jan 29, 2012

### ArcanaNoir

1. The problem statement, all variables and given/known data

In order to advance on a problem I'm working, I need to covert this ellipsoid from cartesian to spherical coordinates.
$$\frac{x^2}{a^2} +\frac{y^2}{b^2} +\frac{z^2}{c^2} = 1$$

2. Relevant equations

$$x^2 +y^2+z^2= \rho ^2$$
$$x=\rho sin \phi cos \theta$$
$$y= \rho sin \phi sin \theta$$
$$z= \rho cos \phi$$

3. The attempt at a solution

I'm not sure how to use those formulas because they look like they would only work with a sphere. I don't know. It's been a semester since calc three and we didn't do spherical coordinates anyway. What do I do?

2. Jan 29, 2012

### ArcanaNoir

using what I foud here: http://math.wikia.com/wiki/Ellipsoid

would I have
$$x=asin\phi cos \theta$$
$$y=bsin \phi sin \theta$$
$$z= ccos\phi$$

Thus, $$\rho ^2= a^2 sin^2 \phi cos^2 \theta + b^2 sin^2 \phi sin ^2 \theta + c^2 cos ^2 \phi$$ ?

3. Jan 30, 2012

### I like Serena

Looks like you've solved it! :)