Question

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.

Answer 1

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

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.