(Solved): Consider the surface defined by \[ -3 x^{2}+y^{2}-2 z^{2}=9 . \] (a) (5 points) Sketch (roughly) t ...

Consider the surface defined by \[ -3 x^{2}+y^{2}-2 z^{2}=9 . \] (a) (5 points) Sketch (roughly) the cross-sections of this surface at \( y=\pm 3, \pm 4, \pm 5 \). (b) (3 points) For which values of \( k \) does the surface have no intersection with the plane \( y=k \) ? (c) (2 points) Sketch the surface.