Let H be the hyperboloid of one sheet, given by x2 + y2 - z2 = 1.

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 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.