Question

The locus of a point so that sum of its distance from two given perpendicular lines is equal to $2$ units in the first quadrant, is

• A. $x+y+2=0$
• B. $x+y=0$
• C. $x+y=2$
• D. none of these

Answer 1

The correct option is C

$x+y=2$

Explanation for the correct option

Let the $x-$axis and $y-$axis be the two perpendicular lines

Let $P(x_1,y_1)$ be the required point.

Draw $PM$ and $PN$ perpendicular to $x-$axis and $y-$axis

Given $PM+PN=2$

But $PM=y_1,PN=x_1$

So $x_1+y_1=2$

Therefore, the locus is $x+y=2$.

Hence, the correct Option is (C) .