Radius Of Curvature In Parametric Form

Radius of Curvature in Parametric Form:

Let x = f (t) and y = g (t) be the Parametric equations of a curve C and P ( x, y) be a given point on it. Then

Substituting the values of dy/dx and d²y/dx² in the Cartesian form of the radius of curvature of the curve y = f (x) in the above equations.

∴

This is the Cartesian form of the radius of curvature in the parametric form.