UPSC NDA 2 2021 Mathematics Solved Paper

Concept:The equation $z = 0$ represents the XY-plane.So any equation of the form $z = c$ (constant) describes a plane parallel to the XY-plane.Explanation:A point $P(x, y, z)$ moves so that $z = 7$ always.Here $x$ and $y$ can take any real values, while $z$ is fixed at $7$.This set of points forms a flat surface, not a line.The XY-plane has equation $z = 0$.Since $z = 7$ differs only by a constant, it is a plane parallel to the XY-plane.Thus, the locus is a plane parallel to the XY-plane.Answer:D. plane parallel to xy - plane