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.