Engineering Board Exam Reviewer · Orthogonal Trajectories · medium

Find the orthogonal trajectories of the family of parabolas y2=Cx.

  1. x2 + 2 y2 = K
  2. 2 x2 + y2 = K
  3. x2 + y2 = K
  4. 2 x2 - y2 = K

Answer

B. 2 x2 + y2 = K

Solution

Differentiate y2=Cx: 2ydy/dx=C=y2/x /dx=y/2x. Orthogonal family: dy/dx=-2x/y. Then y,dy=-2x,dx 2/2=-x2+c 2x2+y2=K.

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