The evolute of a curve R(t) is the locus of the centers of curvature of the curve. Using the parametric formulas, show that the tangent to the evolute is normal to the original curve.
I know that the evolute is e(t) = R(t) + N(t)/k(t). I then take the derivative to find the tangent and get e'(t) = R'(t) - (k'(t)N(t))/(k(t))^2 + N'(t)/k(t).
I know I need to take the dot product to show that this equation is perpendicular to the tangent of the original curve. However, I think I am missing something. Do I need to reparameterize the curves in terms of s?