Eliminate Parameters to Find Ellipsoid Cartesian Equation

[andmcg]

Homework Statement

Eliminate the parameters u and v to obtain a Cartesian equation, thus showing that the given vector equation represents a portion of the surface named. Also, compute the fundamental vector product dr/du x dr/dv in terms of u and v.

Homework Equations

Ellipsoid
r(u,v) = asinucosvi + bsinusinvj + ccosuk

The Attempt at a Solution

I can find the cross product easy enough(abcsinu((sinucosv/a)i+(sinusinv/b)j+(cosu/c)k), but how should I go about getting rid of the parameters?

 

[Mark44]

Let x = asinu*cosv, y = bsinu*sinv, and z = ccosu.

You can combine x and y by using the identity sin^2(t) + cos^2(t) = 1. That's where I would start.