If the distance of any point $(x,y)$ from the origin is defined as $$d(x,y)=max(|x|,|y|)$$, $d(x,y)=a$, non zero constant,then the locus is___.
In question the equation for d is the max absolute value of the coordinate (whether x or y). So if we take square whose center is the origin and of side length 2a then it satisfies the given condition as whatever point we choose on square it will have x or y coordinate to be $a$.
Is this right? Because answer given by the test solution states it to be straight line(Multi choice questions test).