If the distance of any point P(x, y) from the origin is defined as d(x, y) = Max.|x|,|y|  and  d(x, y) = a (non zero constant), then the locus of the P is

d(x, y) = Max. |x|,|y| .....(i)But d(x, y) = a      ..... (ii)From (i) and (ii),  a = Max.  If |x| > |y|, then a = |x|  x = ± aIf |y| > |x|, then a = |y|  y = ± a Hence locus of  P represents a square