For each of the following quadric surfaces find principal axes; identify the surface; sketch the surface with respect to principal aces; find the points on the surface.

part a,d,g.

4. For each of the following quadric surfaces find principal axes; identify the surface; sketch the surface with respect to principal axes; find the points on the surface, if any, which are farthest from and closest to the origin: a) 2x2 + 2y2 + 522 + 2xy + 4xz + 4yz =1; b) x2 + y2 + 222 - 2xz - 2yz = 1; c) 422 + 2 xy + 6xz + 6yz =1; d) x2 + y2 + 22 - 4xy - 4acz - 4yz =3; e) 2ac2 - 2 - 22 - 4xy - 4xz - 8yz = 1; f) -822 + 2xy + 4xz - 4yz =1; g) 3x2 + 5y2 + 422 + 4xz + 4yz = 28