A line segment of length 2 moves in the xy-plane such that it always touches both the coordinate axes (see the image below). Find the area of the region swept out by the line segment.

0 votes

16-4*pi

Since we have tangents at the points where the curves meet the axes, curves can only be quarters of the circle radius 2. This is further supported by x^2+y^2=4 which is true for any position of the line. One quarter of the shaded area= area of square side 2 minus one quarter of the area of the circle radius 2 i.e. (4-pi). Hence the total shades area =16-4*pi

...