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Elimating parameters

  • Thread starter andmcg
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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?
 

Answers and Replies

  • #2
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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.
 

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