The straight line $\frac{x}{a}+\frac{y}{b}=1$ cuts the coordinate  axes at 

$A$ and $B.$ The equation of the circle passing through O ( 0, 0),

$A$ and $B,$ is

detailed solution

Correct option is A

The straight line xa+yb=1 cuts the coordinate axes at A (a, 0) and B (0, b).Let x2+y2+2gx+2fy+c=0                                (i)be the circle passing through O, A and B. Then,0+c=0                                        (ii)a2+2ga+c=0                             (iii)b2+2fb+c=0                             (iv)Solving (ii), (iii) and (iv), we obtaing=−a2, f=−b2 and c=0Substituting these values in (i), we obtain the equation of therequired circle as x2+y2−ax−by=0