Cal3 Homework: Vector Value Function on Ellipsoid

[cthor]

Homework Statement

Find the vector value function whose graph is the indicated surface.

Homework Equations

The ellipsoid (x^2)/9 + (y^2)/4 + z^2 = 1

The Attempt at a Solution

r(u,v)= (u^2)/9i + (v^2)/4j + (1-(u^2)/9-(v^2)/4)^(1/2)k

 

[Kreizhn]

Just use a spherical coordinate system to paramaterize the surface.

let $$\sigma(\theta,\phi) = (3\sin\theta\sin\phi, 2\sin\theta\cos \phi, \cos\theta )$$

 

[cthor]

is there any way you can do it in rectangular coordinates or polar system? Thanks

 

[Kreizhn]

The easiest way to do that in Cartesian coordinates would be

$$\sigma(x,y) = \left(x, y, \sqrt{1-\frac{x^2}{9} -\frac{y^2}{4} } \right)$$