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QUESTION
It is raining and rainwater is running off an ellipsoidal dome with equation 4x^2+y^2+4z^2=16, where zgt;=0.
It is raining and rainwater is running off an ellipsoidal dome with equation 4x^2+y^2+4z^2=16, where z>=0. Given that gravity will cause the raindrops to slide down the dome as rapidly as possible, describe the curves whose paths the raindrops follow.
