Final answer:
The equation of the circle is (x + 4)^2 + (y - 3)^2 = 64.
Step-by-step explanation:
To find the equation of the circle with center (-4, 3) and passing through the x-axis at (-8), we can use the standard form of the equation of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. In this case, the center is (-4, 3) and the radius is the distance from the center to the x-axis, which is 8 units. Substituting these values into the equation, we get (x + 4)^2 + (y - 3)^2 = 64. Therefore, the correct equation is (x + 4)^2 + (y - 3)^2 = 64.