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If the sum of the distances of a point f...

If the sum of the distances of a 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

A

square

B

circle

C

straight line

D

two intersecting lines

Text Solution

Verified by Experts

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.
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