1. **State the problem:** We are given the equation $$x^2 + y^2 - 4y + 4 = 100$$ and need to identify the shape and its properties. 2. **Rewrite the equation:** Notice that the terms involving $y$ can be grouped to complete the square: $$x^2 + (y^2 - 4y + 4) = 100$$ 3. **Complete the square:** The expression $y^2 - 4y + 4$ is a perfect square: $$y^2 - 4y + 4 = (y - 2)^2$$ So the equation becomes: $$x^2 + (y - 2)^2 = 100$$ 4. **Identify the shape:** This is the standard form of a circle equation: $$(x - h)^2 + (y - k)^2 = r^2$$ where the center is at $(h, k)$ and radius is $r$. 5. **Find center and radius:** Comparing, we get: Center: $(0, 2)$ Radius: $$r = \sqrt{100} = 10$$ 6. **Conclusion:** The graph is a circle centered at $(0, 2)$ with radius $10$. This matches the problem statement's description.