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.

Sum of the distances of a point from two perpendicular lines is 3. The area enclosed by the locus of the point is:

If the sum of the squares of the distance of a point from the three coordinate axes is 36, then find its distance from the origin.

A point moves so that its distance from y-axis is half of its distance from the origin.Find the locus of the point.

If the sum of the distances of a moving point from two fixed points (ae, 0) and (-ae, 0) be 2a , prove that the locus of the point is: x^2/a^2+ y^2/(a^2 (1-e^2) =1