Engineering Board Exam Reviewer · Orthogonal Trajectories · medium

Find the orthogonal trajectories of the family of curves y=Cx3.

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

Answer

D. x2 + 3 y2 = K

Solution

From y=Cx3: dy/dx=3Cx2=3y/x. Orthogonal family: dy/dx=-x/3y. Then 3y,dy=-x,dx 3y2/2=-x2/2+c x2+3y2=K.

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