## Radius of Curvature For a Curve y(x)

The position vector of a point on the curve isso

whereis the length along the curve.

and

The Frenet formula giveswhere %rho is radius of the curvarure and hence

The position vector of a point on the curve isso

whereis the length along the curve.

and

The Frenet formula giveswhere %rho is radius of the curvarure and hence