The equation of the circle of center (-8,0) and radius 4 described in this problem is given by:
[tex](x + 8)^2 + y^2 = 16[/tex].
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The circle is tangent to x=-12 and x=-4 and the x-axis, hence the coordinates of the center is given by:
[tex]x_0 = \frac{-12 - 4}{2} = -8, y_0 = 0[/tex]
The radius is given by:
[tex]r = |-12 - (-8)| = |-8 - (-4)| = 4[/tex]
Hence the equation of the circle of center (-8,0) and radius 4 described in this problem is given by:
[tex](x + 8)^2 + y^2 = 16[/tex]
More can be learned about the equation of a circle at https://brainly.com/question/24307696
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