1. The problem states that circle A is given by the equation $$x^2 + (y - 1)^2 = 49$$. This represents a circle centered at $(0,1)$ with radius $7$ because the general form of a circle is $$(x - h)^2 + (y - k)^2 = r^2$$ where $(h,k)$ is the center and $r$ is the radius. 2. Circle B is obtained by shifting circle A down 2 units. Shifting down means subtracting 2 from the $y$-coordinate of the center. 3. The new center of circle B is therefore $(0, 1 - 2) = (0, -1)$. 4. The radius remains the same, $7$, so the equation of circle B is $$x^2 + (y - (-1))^2 = 49$$ which simplifies to $$x^2 + (y + 1)^2 = 49$$. 5. Comparing this with the options given, option D is $$x^2 + (y + 1)^2 = 49$$, which matches our derived equation. Final answer: D) $$x^2 + (y + 1)^2 = 49$$