The equation of the circle given is:

$(x - 8)^2 + (y + 4)^2 = 4$

This is a circle in standard form $(x - h)^2 + (y - k)^2 = r^2$, where:

• $(h, k)$ is the center of the circle
• $r$ is the radius of the circle

From the equation:

• The center of the circle is $(8, -4)$.
• The radius is $\sqrt{4} = 2$.

Now, let's identify the circle on the graph:

1. Look for a circle centered at $(8, -4)$.
2. Check if the circle has a radius of 2 units.

By examining the graph:

• The circle labeled "D" appears to have its center at $(8, -4)$.
• The radius of circle "D" is 2 units.

Thus, the circle "D" corresponds to the equation $(x - 8)^2 + (y + 4)^2 = 4$.

Answer: Option D

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you derive the center and radius of a circle from its equation?
2. What is the general equation of a circle, and how does it differ from other conic sections?
3. How would the graph change if the equation were $(x - 8)^2 + (y + 4)^2 = 9$?
4. What happens to the circle if you change the signs in the equation, e.g., $(x + 8)^2 + (y - 4)^2 = 4$?
5. How can you graph a circle given its equation in standard form?

Tip: When identifying circles on a coordinate plane, always verify both the center and the radius to ensure accuracy.