Let the analytical expression of L be y=kx and the coordinate of point P be (x, kx), then according to the symmetry of the image, the coordinate of point Q is (-x, -kx).

Distance between p and q = 2x * sqrt (k 2+1)

Because y=kx= 1/x

So x=sqrt( 1/k)

Distance between p and q =2sqrt(k+ 1/k)

k & gt0,k+ 1/k=(k^2+ 1)/k=(k- 1)^2/k+2

(k- 1)^2/k>； =0 so k+1/k > =2

The distance between p and q >; =2sqrt(2), that is, k= 1, and the minimum PQ length is 2sqrt(2).