Consider the surface S with equation x2 C y2 C 4z2 D 16. (a)

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Consider the surface S with equation x2 C y2 C 4z2 D 16. (a) Find an equation for the tangent plane to S at the point .a

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Consider the surface S with equation x2 C y2 C 4z2 D 16. (a) Find an equation for the tangent plane to S at the point .a; b; c/ on S. (b) For which points .a; b; c/ on S does the tangent plane to S at .a; b; c/ pass through the point .0; 0; 4/? Describe this set of points geometrically. (c) For which points .a; b; c/ on S is the tangent plane to S at .a; b; c/ parallel to the plane x C y C 2 p2z D 97?

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