1. **State the problem:** We need to find the equation of a circle representing the perimeter of a circular park with center at $(2, -3)$ and a point on the edge at $(4, -1)$. 2. **Recall the formula for a circle:** The equation of a circle with center $(h, k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. **Identify center and radius:** Here, the center is $(h, k) = (2, -3)$. 4. **Calculate the radius $r$:** The radius is the distance from the center to the point on the edge: $$ r = \sqrt{(4 - 2)^2 + (-1 + 3)^2} = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} $$ 5. **Write the equation:** Substitute $h=2$, $k=-3$, and $r^2 = 8$ into the formula: $$ (x - 2)^2 + (y + 3)^2 = 8 $$ 6. **Match with options:** This matches option D. **Final answer:** Option D: $\boxed{(x - 2)^2 + (y + 3)^2 = 8}$