This means we get (for free) a bunch of lines inside planes parallel to the y-axis. Even better, every plane tangent to this surface will automatically be parallel to the y-axis. So, we just need to find which of these planes is/are parallel to the z-axis. (Note that saying the yz-plane is the same as saying the plane perpendicular to the x-axis.) This reduces it to a pre-calculus question: Find the point in the x-z plane (perpendicular to the y-axis) where the slope of the parabola is the same as the slope of the z-axis, ie is zero. Since this parabola is lined up with the x- and z-axes (ie, is not diagonal), this is the same as saying, "find the vertex", which also happens to be centered on the x-axis in this case.