Question

If the distance of any point $(x,y)$ from $(0,0)$ is defined as $d(x,y)=max\parallel x|,|y\parallel$,then locus of the point $(x,y)$ such that $d(x,y)=1$, is

• A. an ellipse
• B. a circle
• C. a triangle
• D. a square of area 4 square units.

Answer 1

The correct option is D a square of area 4 square units.

Given $d(x,y)=1$
Now $d(x,y)=max\parallel x|,|y\parallel$
$\Rightarrow \left|x\right|\le 1,and\left|y\right|\le 1$
$\Rightarrow -1\le x\le 1and-1\le y\le 1$
$\Rightarrow$ locus of $(x,y)$ is square having its vertices at $(1,1),(-1,1),(-1,-1)(1,-1)$
$\therefore$ Each side of squre is 2 units
$\Rightarrow$ Area of squre$=2\times 2=4$ square units
Hence choice (D) is correct answer.