Question

If the sum of the distances of a variable point from two perpendicular lines in a plane is $1$, 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 $P$ is a variable point whose coordinates are $(h,k)$ and x-axis and y-axis are two perpendicular lines.
So $PM+PN=1$
$\Rightarrow \left|k\right|+\left|h\right|=1$
$\Rightarrow \left|x\right|+\left|y\right|=1$
which is required focus and is square