The problem asks to identify the center and radius of the circle given by the equation $(x+3)^2 + y^2 = 9$.

GeometryCirclesEquation of a CircleCoordinate Geometry
2025/5/7

1. Problem Description

The problem asks to identify the center and radius of the circle given by the equation (x+3)2+y2=9(x+3)^2 + y^2 = 9.

2. Solution Steps

The general equation of a circle with center (h,k)(h, k) and radius rr is:
(xh)2+(yk)2=r2(x - h)^2 + (y - k)^2 = r^2
Comparing the given equation (x+3)2+y2=9(x+3)^2 + y^2 = 9 with the general equation, we can rewrite the given equation as:
(x(3))2+(y0)2=32(x - (-3))^2 + (y - 0)^2 = 3^2
Thus, we have h=3h = -3, k=0k = 0, and r=3r = 3. Therefore, the center of the circle is (3,0)(-3, 0) and the radius is 33.

3. Final Answer

Center: (3,0)(-3, 0)
Radius: 33

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