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The evolute of a curve is the locus of

  • A.its centres of curvature
  • B.its points of inflexion
  • C.the feet of its normals on a fixed line
  • D.its points of maximum curvature

Answer: A

Each point of a curve has a centre of curvature, lying on the normal at a distance \( \rho \) on the concave side. As the point moves along the curve the centre traces the evolute, and the original curve is then one involute of it. Inflexion points, where the curvature vanishes, send the centre off to infinity

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