7. Let 11. be the hyperboloid of one sheet, given by x2 + y2 - z2 = 1.

(a) Prove that at every point

(a,

b, c) E 11.,11. has a tangent plane whose normal is given by (-a, -b, c).

(b) Find an equation of each plane tangent to 11. that is perpendicular to the xy plane.

(c) Find an equation of each plane tangent to 11. that is parallel to the plane x+y-z=1.