The correct answer is:

(b) The radius of the circle that best approximates the curve at that point.

This definition aligns with the concept of the radius of curvature, which describes the radius of an osculating (approximating) circle that "fits" the curve at a specific point. This circle has the same tangent and curvature as the curve at that point, providing an accurate local representation.

Would you like further details, or do you have any questions?

Here are some related questions to deepen understanding:

1. How do you calculate the radius of curvature for a curve given a specific function?
2. What is the relationship between curvature and radius of curvature?
3. How does the radius of curvature vary for straight lines versus circles?
4. What is an osculating circle, and how does it relate to curvature?
5. How can the radius of curvature help in understanding the behavior of a curve?

Tip: The radius of curvature provides insights into how sharply a curve bends at any given point.