To complete the equation of a circle, we use the standard form:

$(x - h)^2 + (y - k)^2 = r^2$

Where:

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

Given:

• Center: $(-8, 2)$ → So, $h = -8$ and $k = 2$.
• Radius: $r = 3$.

Substitute these values into the equation:

$(x - (-8))^2 + (y - 2)^2 = 3^2$

Simplifying:

$(x + 8)^2 + (y - 2)^2 = 9$

Thus, the equation of the circle is:

$(x + 8)^2 + (y - 2)^2 = 9$

Would you like more details or have any questions?

---

Here are 5 related questions to expand on this topic:

1. What is the general equation of a circle if the radius is unknown but the center is given?
2. How do you find the radius of a circle given its equation in standard form?
3. Can a circle have a radius of 0? What would its equation be?
4. How would the equation change if the center was at the origin (0, 0)?
5. How do you find the equation of a circle passing through a specific point?

Tip: The distance between any point on the circle and its center is always the radius.