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___.

My attempt

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).

  • 2
    $\begingroup$ Yep, you're right. $\endgroup$ – Frpzzd Oct 1 '18 at 19:25

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