WBJEE 2013 Math Solved Paper

Circle passes through (0,0)
so, x2 + y2 + 2gx + 2fy = 0
(2, 6) & (6, 2) lies on it so,
22 +62 + 4g + 12f = 0 .... (1)
22 + 62 12g + 4f = 0 .... (2)
⇒ From (1) & (2)
g = f = –5/2
Eqn. of circle is x2 + y2 – 5x – 5y = 0
For y = 0, x (x - 5) = 0 ⇒ x = 0, x = 5
OP = 5