Question: Let H be the hyperboloid of one sheet, given by x2 + y2 - z2 = 1. a) Use Exercise 11.6.9 to prove that at

Let H be the hyperboloid of one sheet, given by x2 + y2 - z2 = 1.
a) Use Exercise 11.6.9 to prove that at every point (a, b, c) ∈ H, H has a tangent plane whose normal is given by (-a, -b, c).
b) Find an equation of each plane tangent to H which is perpendicular to the xy-plane.
c) Find an equation of each plane tangent to H which is parallel to the plane x + y - z = 1.

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a By Exercise 1169 the normal of H at a b c is parallel to F 2x 2y2z Hence we ca... View full answer

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