Question: Let S be the surface with equation (z-4)^2 = 4x^2 + 4y^2. 1. Find an equation of each trace of S on the coordinate

Let S be the surface with equation (z-4)^2 = 4x^2 + 4y^2.

Let S be the surface with equation (z-4)^2 = 4x^2 + 4y^2. 1. Find an equation of each trace of S on the coordinate planes and on the planes z = 4 and z = 8, then identify each trace. 2. Identify the type of quadric surface for S. 3. Provide a hand-drawn sketch of S using the traces obtained in (question 1). Label all important points found on each trace. 4. Viewing S as a surface of revolution, find an equation of a generating curve on the yz-plane and determine its corresponding axis of revolution.

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