Definition of Radius and Circle of Curvature
For a smooth space curve, the curvature measures how fast the curve is bending or changing direction at a given point. The more closed is the curve, the larger is the curvature. The curvature of a line is zero.
The radius of curvature is the reciprocal of the curvature. It is the radius of a circle tangent to the curve that best fits at each point.
Verify that the given formula is correct for curves in the plane.