# The locus of a point $(x,y,z)$ for which $z=k$ is a ?

$\begin {array} {cc} (a)\:A\:plane\:||\:to\:xy\:plane\:at\:a \:distance\:k\:from\:it &(b)\:A\:plane\:||\:to\:yz\:plane\:at\:a\: distance\:k\:from\:it\\ (c)\:A\:plane\:||\:to\:zx\:plane\:at\:a\: distance\:k\:from\:it & (d)\: A\:plane\:||\:to\:Z\:axis\:at\:a\:distance\:k\:from\:it. \end {array}$

Given that the point on the locus is such that its $z$ coordinate is constant $k$.
$\therefore$ the point moves in a plane parallel to $xy$ plane.
which is at a constant distance $k$ from it.