Let $(x,y)$ be any arbitrary point on a curve and the distance from origin of the point $(x,y)$ has been defined as $d$ such that $$d=\max(|x|,|y|)$$ and $$d=k$$ such that $k$ is a non-zero positive constant.
then what would be the locus of the point $(x,y)$.
I tried to solve the question using basic properties of absolute values.
$$|x| \le k ; |y| \le k$$ $$\Rightarrow -k \le x \le k ; -k \le y \le k $$
According to this must be a square formed by the lines $$x=k; x=-k; y=k; y=-k$$ But my book mentions the answer to be a straight line. Can anybody help me over this issue?