Chapter 8.2, Problem 21E

a. Sketch the following three surfaces:
$x_1^2+4x_2^2+9x_3^2=1$
$x_1^2+4x_2^2-9x_3^2=1$
$-x_1^2-4x_2^2+9x_3^2=1$
Which of these are bounded? Which are connected? Label the points closest to and farthest from the origin (if there are any).
b. Consider the surface
$x_1^2+2x_2^2+3x_3^2+x_1{x}_2+2x_1{x}_2+3x_2{x}_3=1$
Which of the three surfaces in part (a) does this surface qualitatively resemble most? Which points on this surface arc closest to the origin? Give a rough approximation; you may use technology.