Answer
A parabola in the plane $x=1$ (which is parallel to the yz plane).
Work Step by Step
$x=1$ is a plane parallel to the yz plane, passing through $(1,0,0).$
$z=y^{2}$ intersected with any plane $x=k$, is a parabola.
So, this is a parabola in the plane $x=1$ (which is parallel to the yz plane).
