Question

If the distance of any point $(x,y)$ from the origin is given by $d(x,y)$=$max\{|x|,|y|\}$. Let $P(x,y)$ be such that $d(x,y)=2$ then the locus of $P$ is:

• A. a circle
• B. a square
• C. a straight line
• D. None of these

Answer 1

The correct option is B a square

Given, $d(x,y)$=$max\{|x|,|y|\}$.

Also given $d(x,y)=2$.

According to the definition of $d(x,y)$ we have,

$|x|\le 2$ ......(1) and

$|y|\le 2$ ......(2).

If we plot (1) and (2) we get, a square in $x-y$ plane.