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  4. The locus of a point P which moves such that the sum of its distances from two perpendicular lines is equal to 1 is a

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Q. The locus of a point $P$ which moves such that the sum of its distances from two perpendicular lines is equal to 1 is a

TS EAMCET 2021

Solution:

Let $P(x, y)$ be any point.
Then, $|P A|+|P B|=1$
image
$\Rightarrow|x|+|y|=1$
Lines are $x+y=1, x-y=1$
$-x+y=1,-x-y=1$
image
Which forms a square