For a concave mirror, when an object is placed at the center of curvature (C), the image formation follows the mirror formula: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$, where f is the focal length, u is the object distance, and v is the image distance. The center of curvature is at a distance of 2f from the mirror, so u = -2f (using the Cartesian sign convention). Substituting into the formula: $\frac{1}{f}=\frac{1}{v}+\frac{1}{-2f}$. Solving for v gives v = -2f. This means the image is formed at the same point as the object, at C. The image is real, inverted, and the same size as the object.

Final answer: at C.