A point moves in the xy-plane such that the sum of its distances from the two mutually perpendicular lines is always equal to 5 units. The area (in square units) enclosed by the locus of the point is

Explanation

Here, the point moves in the xy-plane such that the sum of its distances from the two mutually perpendicular lines is always equal to 5 units.

`:. |x|+|y| = 5`

`=>x+y = 5, x-y = 5, -x+y = 5, -x-y = 5`

If we draw these lines on coordinate axis, it will a square of side `5sqrt2(sqrt(5^2+5^2))` units.

Please refer to video to see the square in the diagram.

`:.` Area enclosed = Area of square `= (5sqrt2)^2 = 50` square units