Answer
(a) Parabola
(b) Parabolic cylinder along the z-axis
(b) Parabolic cylinder along the x-axis
Work Step by Step
(a) In the xy-plane, $y=x^{2}$ represents the standard equation of a parabola.
(b) As a surface in the 3-dimensional xyz-space, $y=x^{2}$ represents a parabola in the x-y plane extended infinitely along the z-axis (parabolic cylinder).
(c) The equation $z=y^{2}$ represents a parabola in the yz-plane extended infinitely along the x-axis (parabolic cylinder).
