Step-by-Step Solution
Key Concept: Using the locus of a point satisfying a parametric condition on a circle
Let point $M = (h, k)$. Then $B = (\frac{h+k}{2}, \frac{k+4}{2})$ which lies on the given circle. Substituting: $(\frac{h}{2})^2 + 9(\frac{k}{2}) + (\frac{k+4}{3} - 3)^2 = 0$, which simplifies to $k^2 + 18k + (k - 3)^2 = 0$ or $x^2 + 18x + (y - 3)^2 = 0$.
Correct Answer: 2