The equation of a circle in standard form is given by:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

where \((h, k)\) is the center of the circle and \(r\) is the radius.

Given:
- Center: \((-3, 8)\)
- Radius: \(3\)

Substitute these values into the standard form equation:

\[
(x - (-3))^2 + (y - 8)^2 = 3^2
\]

Simplify:

\[
(x + 3)^2 + (y - 8)^2 = 9
\]

So, the equation of the circle is:

\[
(x + 3)^2 + (y - 8)^2 = 9
\]

Would you like more details or have any questions?

Here are some related questions to explore further:

1. How do you find the center and radius from the equation of a circle?
2. What is the general form of the equation of a circle?
3. How do you convert the general form to the standard form of a circle's equation?
4. What is the significance of the radius in a circle's equation?
5. How do you determine if a point lies on a circle given its equation?
6. Can you derive the equation of a circle given three points on the circumference?
7. How does the equation of a circle change if the circle is translated?
8. What are some real-life applications of the equation of a circle?

**Tip:** Always double-check your substitutions and simplifications when working with equations to avoid small mistakes that can lead to incorrect answers.

Understand how to derive the equation of a circle with center at (-3, 8) and radius 3. Learn the standard form of the equation of a circle and its application in coordinate geometry. Suitable for high school students.

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