The locus of the centre of the circle passing through the origin O and the points of intersection of any line through (a,b)  and the coordinates axis is a

Equation of the line be xl+ym=1  and al+bm=1 . Equation of the circle through (0,0),(l,0)  and (0,m)  is x2+y2−lx−my=0,  centre is (l/2,m/2). Whose locus is a2x+b2y=1 .