Answer
Parabolic cylinder; the trace is the parabola $ y=3x^2 $ in the $ xy $-plane.
Work Step by Step
The equation
$$
y=3x^2
$$
is the equation of a parabolic cylinder.
(See equations on page 691.)
The trace with the plane $ z=27$ is the parabola $ y=3x^2 $ in the $ xy $-plane.
