If the distance of any point $(x,\ y)$ from the origin is defined as $d(x,\ y) =$max $\left\{ |x|,\ |y| \right\},\ d(x,y) = a$, non-zero constant, then the locus is

Question

Dr. Abubacker · Accepted Answer

(b)
$d(x,y) = max\{|x|,\ |y|\}$ …(i)
$but\ d(x,y) = a$ …(ii)
From, Eqs. (i) and (ii),
$a = {max\ }\left\{ |x|,\ |y| ight\}$
If $|x| > |y|,\$ then $a = |x|$
$	herefore\ x = \pm a$
$and\ if\ |y| > |x|,\$ then $a = |y|$
$	herefore y = \pm a$
Therefore, locus represents a straight line

Q. If the distance of any point $(x,\ y)$ from the origin is defined as $d(x,\ y) =$max $\left\{ |x|,\ |y| \right\},\ d(x,y) = a$, non-zero constant, then the locus is

Explanation

Reviewed by Dr. Abubacker

Want more practice?