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If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point

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Let the coordinates of a moving point P be (a,b)

 It is given that the sum of the distance from the axes to the point is always 1  |x|+|y|=1 

  ±x±y=1 -x-y=1, x+y=1, -x+y=1 and x-y=1

 Hence, these equations gives us the locus of the point P which is a square.

 

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