Question

A point $P$ moves in such a way that sum of its perpendicular distances from two perpendicular lines in its plane is always $2$ units. Then find the area of region bounded by locus of $P$ .

Answer 1

Let $x$ axis and $y$ axis be the two perpendicular lines. Let $P$ be $\left(h , k\right)$

then $\left|h\right|+\left|k\right|=2$
So locus of $P$ is $\Rightarrow \left|x\right|+\left|y\right|=2$
Which represents four lines forming a square

Area $=4\left(\frac{1}{2} \cdot 2 \cdot 2\right)=8$ sq. units