Question: 1. Fix a, b, c > 0. Consider the ellipsoid E = {(x, y, 2) E R3 + + (= 1}. (a) Prove that E

1. Fix a, b, c > 0. Consider the ellipsoid E = {(x, y, 2) E R3 + + (= 1}. (a) Prove that E is a smooth surface. (Hint: Adapt the surface patches for the sphere which were given in exercise 4.1.2.) (b) Find one of the (non-trivial) transition maps between allowable patches in your atlas. (c) Find the tangent plane Tp E for p = (0, b V/2'

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