The line L passes through point P (2,1) and intersects with the positive half axis of X axis and Y axis at two points a and B respectively. O is the origin. When the perimeter of triangle OAB is the minimum, the equation of line L is obtained

The line L passes through point P (2,1) and intersects with the positive half axis of X axis and Y axis at two points a and B respectively. O is the origin. When the perimeter of triangle OAB is the minimum, the equation of line L is obtained

Let the equation of l be Y-1 = K (X-2), then the intersection points of L and X, Y axes are (K / 2k-1,0) and (0,1-2k) respectively
From the triangle area formula and the mean inequality
S=0.5[-4k-(1/k)+4]>=0.5(2X2+4)=4
So the minimum area is 4