https://file.aiquickdraw.com/mathbot/file/1726275101308kjqdexw8.jpg

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.

Which graph has the equation: (x - 8)^2 + (y + 4)^2 = 4?

Learn how to identify a circle on a graph based on its equation (x - 8)^2 + (y + 4)^2 = 4. This problem involves recognizing the center and radius of a circle, and it is suitable for students in Grades 8-10.

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