Straight Line and Pair of Straight Lines 1 Question 36
36. If the sum of the distance of a point from two perpendicular lines in a plane is 1 , then its locus is
(a) square
(b) circle
(c) straight line
(d) two intersecting lines $(1992,2 M)$
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Solution:
- By the given conditions, we can take two perpendicular lines as $x$ and $y$ axes. If $(h, k)$ is any point on the locus, then $|h|+|k|=1$. Therefore, the locus is $|x|+|y|=1$. This consist of a square of side 1 .
Hence, the required locus is a square.
