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The envelope of a family of curves is a curve that

  • A.is the locus of the centres of every member
  • B.touches every member of the family
  • C.cuts every member of the family at right angles
  • D.passes through the singular points of every member

Answer: B

The envelope is tangent to each curve of the family at some point, and is found by eliminating the parameter between \( F(x,y,c) = 0 \) and \( \partial F/\partial c = 0 \). The orthogonal-crossing curve is a member of the orthogonal family instead, and the locus of centres of curvature is the evolute

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