Let the general equation of the circle be $x^2 + y^2 + 2gx + 2fy + c = 0$. Since the circle passes through the origin $(0,0)$, substituting these coordinates gives $0^2 + 0^2 + 2g(0) + 2f(0) + c = 0$, which implies $c=0$. Since the circle makes an intercept of length $a$ on the positive x-axis, it passes through $(a,0)$. Substituting $(a,0)$ into the circle's equation ($c=0$): $a^2 + 0^2 + 2g(a) + 2f(0) + 0 = 0 \Rightarrow a^2 + 2ga = 0$. Since $a \neq 0$, we get $a + 2g = 0 \Rightarrow 2g = -a$. Similarly, it makes an intercept of length $b$ on the positive y-axis, so it passes through $(0,b)$. Substituting $(0,b)$ into the circle's equation ($c=0$): $0^2 + b^2 + 2g(0) + 2f(b) + 0 = 0 \Rightarrow b^2 + 2fb = 0$. Since $b \neq 0$, we get $b + 2f = 0 \Rightarrow 2f = -b$. Substituting the values of $2g$, $2f$, and $c$ back into the general equation, we get $x^2 + y^2 - ax - by = 0$.

Option A, C, and D do not satisfy the conditions derived (e.g., passing through the origin or correctly matching the intercepts).