Answer: $\mathbf A$
If a circle passes through the origin and the centre lies on the $\mathrm x$ axis then the length of the abscissa will be equal to the circle's radius and the ordinate(y-coordinate) will be $0$.
So, the equation of the circle will be of the form:
$\mathrm {(x-a)^2 + y^2 = a^2}$
$\Rightarrow \mathrm{ x^2 + y^2 -2ax = 0}$
$\therefore \mathbf A $ is the right option.