Question: 59. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. The graph of

59. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. The graph of the equation y = 2 in R is both a cylinder and

59. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. The graph of the equation y = 2 in R is both a cylinder and a quadric surface. b. The xy-traces of the ellipsoid x + 2y + 3z = 16 and the cylinder x+2y = 16 are identical. c. Traces of the surface y = 3x - z in planes parallel to the xy-plane are parabolas. d. Traces of the surface y = 3x - z in planes parallel to the xz-plane are parabolas. e. The graph of the ellipsoid x + 2y + 3(z - 4) = 25 is obtained by shifting the graph of the ellipsoid x+2y+3z = 25 down 4 units.

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