Hi aspirant,

Evolute. An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute.

That means: at points with maximal or minimal curvature the evolute has cusps (s. ... The normals of the given curve are tangents to the evolute. Hence: the evolute is the envelope of the normals of the given curve. At sections of the curve with or the curve is an involute of its evolute.

Put the result into the formula at (dy/dx)^2. Plug the second derivative of your curve equation into the formula for finding the radius of curvature. Put the second derivative into the formula at d^2y/dx^2. Solve the equation for a point “x” along your curve by replacing the variable "x" with a numerical value.

All the very best!!