Final answer:
The center of the circle is (-1/3, 0), and the radius of the circle is 3 √3 or approximately 5.20 units.
Step-by-step explanation:
The given equation of the circle is (x+1/3)²+y²=27. To identify the center and radius of the circle, we need to bring the equation to the standard form of a circle's equation: (x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius.
In the given equation, we can compare it directly to the standard form. Here, the term (x+1/3)² suggests that our h value is -1/3 and since there is simply y², it implies that our k value is 0. Therefore, the center of the circle is at (-1/3, 0). For the radius, since the right side of the equation is 27, we can deduce that r² = 27. Taking the square root of both sides, we find that r = 3 √3 or approximately r = 5.20.