A line passing through the point P(4, 2), meets the x-axis and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circum circle of ∆OAB is

Let the coordinates of A and B be (a, 0) and (0, b) respectively. Then, equation of line AB is xa+yb=1Since, it passes through the point P(4, 2)∴4a+2b=1             -----(1)Now, centre of the circumcircle of ∆OAB=a2,b2So, Eq. (1) can be written in the form 2a/2+1b/2=1∴locus of circumcentre is 2x+1y=1 or 2x-1+y-1=1