2011-II-51 – Solving Master

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.

Let $(0, r)$ be the centre of $C$ , where $r$ is the radius of the circle.

$\begin{array}{rcl} \sqrt{(0 - (- 3))^{2} + (r - 1)^{2}} & = & r \\ 9 + r^{2} - 2 r + 1 & = & r^{2} \\ r & = & 5 \end{array}$

Hence, the equation of $C$ is

$\begin{array}{rcl} (x - 0)^{2} + (y - 5)^{2} & = & 5^{2} \\ x^{2} + y^{2} - 10 y + 25 - 25 & = & 0 \\ x^{2} + y^{2} - 10 y & = & 0 \end{array}$