Identify the traces.

The vertical trace in the plane $x=c$ is a circle for all $c.$

The horizontal trace at height $c$ is a circle in the plane $z=c$ for $y=az=\frac{1}{x^2+a^2+1}cz=cc=1x=aa0.$

The vertical trace $in$ the plane $y=ais$ the curve $z=\frac{1}{x^2+a^2+1}.$

The horizontal trace $at$ height $cis$ the origin $in$ the plane $z=c$ for $c=1.$

The vertical trace $in$ the plane $x=ais$ a parabola for all $a.$