Engineering Board Exam Reviewer · Orthogonal Trajectories · medium

Find the orthogonal trajectories of the family of lines y=Cx.

1. x2+y2=C
2. y2-x2=C
3. xy=C
4. y=-x+C

Answer

A. x2+y2=C

Solution

Eliminating C: dy/dx=y/x. The orthogonal family satisfies dy/dx=-x/y y,dy=-x,dx x2+y2=C.

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