Chapter 12: Vectors and the Geometry of Space - Section 12.1 - Three-Dimensional Coordinate Systems - Exercises 12.1 - Page 695: 16

A parabola in the plane $x=1 $ (which is parallel to the yz plane).

$x=1$ 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 (see image below) a parabola in the plane $x=1 $ (which is parallel to the yz plane).