If p is the length of the perpendicular from the origin to the line xa+yb=1 then
1a2+1b2=1p2
1a2+1b2=2p2
1a2-1b2=1p2
1a2+1b2=p2
The perpendicular distance from origin to the line ax +by +c=0 is ca2+b2
The distance from origin to the line xa+yb=1 is p, given p=11a2+1b2
take reciprocals and then squaring both sides