Question

If the sum of the distances of a point from two perpendicular lines in a plane is a constant, then its locus is

• A. a square
• B. a circle
• C. a straight line
• D. two intersecting lines

Answer 1

The correct option is A a square

Let the two perpendicular lines be axis.
Consider a point $(h,k)$
Sum of distance from axis is constant $=c$
$|h|+|k|=c$
We get four lines $h+k=c,h-k=c,-h+k=c,-h-k=c$ whose intersection forms square with vertices $(c,0),(0,c)(-c,0),(0,-c)$ respectively.