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To find the standard form of the equation of a circle with a given center and radius, we use the formula:

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

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

### Given:
- Center: \((-8, 4)\) (so \(h = -8\) and \(k = 4\))
- Radius: \(r = 6\)

### Step-by-Step Solution:
1. Substitute \(h = -8\), \(k = 4\), and \(r = 6\) into the formula.
   
   \[
   (x - (-8))^2 + (y - 4)^2 = 6^2
   \]

2. Simplify the expression:
   \[
   (x + 8)^2 + (y - 4)^2 = 36
   \]

### Answer:
The standard form of the equation of the circle is:
\[
(x + 8)^2 + (y - 4)^2 = 36
\]

Would you like more details on this process or have any questions?

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### Related Questions:
1. How do you find the radius of a circle if given the standard form equation?
2. What is the general form of a circle’s equation, and how do you convert from standard form?
3. How would you find the center and radius of a circle if given its equation in general form?
4. Can the standard form equation be used for ellipses, and if so, how does it differ?
5. How do you find the equation of a circle given three points on its circumference?

### Tip:
When writing the equation of a circle, always square the radius and double-check that signs are correct for the center coordinates!

Write the standard form of the equation of the circle with the given center (-8,4) and radius r=6.

Learn how to write the standard form of a circle's equation with center (-8, 4) and radius 6. This problem includes key geometry concepts like the equation of a circle formula. Suitable for Grades 9-10.

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