Chapter 13.6, Problem 59E

a.

To determine

Whether the statement “The graph of the equation $y=z^2$ in ${ℝ}^3$ is both a cylinder and quadratic surface” is true or false.

b.

To determine

Whether the statement “The xy-traces of the ellipsoid $x^2+2y^2+3z^2=16$ and the cylinder $x^2+2y^2=16$ are identical ” is true or false.

c.

To determine

Whether the statement “Traces of the surface $y=3x^2-z^2$ in planes parallel to the xy plane are parabola ” is true or false.

d.

To determine

Whether the statement “Traces of the surface $y=3x^2-z^2$ in planes parallel to the xz plane are parabolas” is true or false.

e.

To determine

Whether the statement “The graph of the ellipsoid $x^2+2y^2+3{\left(z-4\right)}^2=25$ is obtained by shifiting the graph of the ellipsoid $x^2+2y^2+3z^2=25$ down 4 units” is true or false.