Ans: B
Since the centre of $C$ lies on the $y$-axis and $C$ touches the $x$-axis, then the point of contact is the origin.
Since the centre of $C$ lies on the $y$-axis and $C$ touches the $x$-axis, then the point of contact is the origin.
Let $(0,r)$ be the centre of $C$, where $r$ is the radius of the circle.
$\begin{array}{rcl}
\sqrt{(0-(-3))^2+(r-1)^2} & = & r \\
9+r^2-2r+1 & = & r^2 \\
r & = & 5
\end{array}$
Hence, the equation of $C$ is
$\begin{array}{rcl}
(x-0)^2 + (y-5)^2 & = & 5^2 \\
x^2 +y^2 -10y + 25 -25 & = & 0 \\
x^2 + y^2 -10y & = & 0
\end{array}$
