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

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

Here:
- \( h = -8 \)
- \( k = 0 \)
- \( r = 4 \)

Substitute these values into the formula:

\[
(x - (-8))^2 + (y - 0)^2 = 4^2
\]

This simplifies to:

\[
(x + 8)^2 + y^2 = 16
\]

So, the correct answer is the fourth option:

\[
(x + 8)^2 + y^2 = 16
\]

Would you like more details or have any questions about this solution?

Here are 5 related questions to deepen your understanding:
1. How would the equation change if the radius were doubled?
2. What is the general formula for the equation of a circle?
3. How does the equation of a circle change if the center is at the origin?
4. Can the center of a circle have negative coordinates, and how does that affect the equation?
5. How do you find the radius of a circle if the equation is already given in standard form?

**Tip:** When writing the equation of a circle, remember that \( (h, k) \) represents the coordinates of the circle's center, and the sign in the equation is always the opposite of the signs of \( h \) and \( k \) in the coordinate form.

Write the standard form of the equation of the circle whose radius is r and whose center is (h, k).
r = 4; (h, k) = (-8, 0)

Learn how to find the standard form of the equation of a circle with a radius of 4 and a center at (-8, 0). This detailed solution covers key geometric concepts and includes step-by-step instructions for solving the equation. Suitable for students in Grades 9-11.

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