Engineering Board Exam Reviewer · Orthogonal Trajectories · easy

Find the orthogonal trajectories of the family of parabolas y=x2+C.

  1. y = K + x/2
  2. y = K - 2 x
  3. y = K - x/2
  4. y = K - 12 x2

Answer

C. y = K - x/2

Solution

From y=x2+C: dy/dx=2x. Orthogonal family: dy/dx=-1/2x y=- 12 |x|+K.

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