Let the circle makes intercepts a with x-axis and b with y-axis. ∴ OA = a and OB = b So the co-ordinates of A are (a, 0) and B are (0, b) Now, the circle passes through three points O(0, 0), A(a, 0) and B(0, b). Putting the co-ordinates of these three points in the general equation of circle $x^2 + y^2$ + 2gx + 2fy + c = 0 .....(i) ⇒ c = 0 (Since Circle passes through point O (0, 0)) Put (a, 0) in (i) $a^2$ + 2ga = 0 ⇒ a(a + 2g) = 0 ⇒ g = $-\frac{1}{2}$ a Put (0, b) in (i) $b^2$ + 2fb = 0 ⇒ b(b + 2f) = 0 ⇒ f = $-\frac{1}{2}$ b Putting these values of g, f and c in (i), we get $x^2 + y^2 + 2 \times -\frac{1}{2} x$ + $2 \times -\frac{1}{2} by + 0$ = 0 ⇒ $x^2 + y^2$ – ax – by = 0 which is the required equation of circle