If the distance of ny 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

Options

A. a circle
B. a square
C. a triangle
D. none of these

Answer

B

Explanation

We have ,
d (x , y) = 1
`implies ` max {|x| , |y|} = 1
`implies | x| le 1` and `|y| = le 1`
`implies -1 le x le 1` and `-1 le y le 1`
`implies ` Locus of (x , y) is the square having its vertices at
(1,1) , (-1,1) , (-1,-1) and (1,-1).