Answer to Question #278884 in Calculus for Vaishnavi

Question

Determine and sketech the set of pairs (x, y) in R×R that satisfy: i)|x|=|y| ii)|x|-|y|=2

Answer 1

i)

$|x|=|y|=>y=x$ or $y=-x$

Two perpendicular lines $y=x$ and $y=-x.$

ii)

$|x|-|y|=2$

$x< 0:$

$$-x-|y|=2=>|y|=-x-2$$

$$y=x+2\ or\ y=-x-2, x\leq-2$$

$x\geq 0:$

$$x-|y|=2=>|y|=x-2$$

$$y=x-2\ or\ y=-x+2, x\geq2$$