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Solve the Problem x236+y281+z24=1\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 81 } + \frac { z ^ { 2 } } { 4 } = 1

Question 196

Essay

Solve the problem.
-Find a parametrization for the ellipsoid x236+y281+z24=1\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 81 } + \frac { z ^ { 2 } } { 4 } = 1 . (Recall that the parametrization of an ellipse x236+\frac { x ^ { 2 } } { 36 } + y281=1\frac { y ^ { 2 } } { 81 } = 1 is x=6cosθ,y=9sinθ,0θ<2π)\left. x = 6 \cos \theta , y = 9 \sin \theta , 0 \leq \theta < 2 \pi \right)

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