Engineering Board Exam Reviewer · Orthogonal Trajectories · medium

Find the orthogonal trajectories of the family of hyperbolas xy=C.

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

Answer

C. x2 - y2 = K

Solution

From xy=C: xdy/dx+y=0 /dx=- yx. Orthogonal family: dy/dx= xy. Then y,dy=x,dx y2=x2+c x2-y2=K.

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