What is the family of orthogonal trajectories to the family of rectangular hyperbolas ()?
Answer and explanation
Correct answer: B.
- Step 1: Differentiate with respect to : .
- Step 2: Replace with to form the differential equation of orthogonal trajectories: .
- Step 3: Separate variables: . Integrate: .
Answer
.
Why not the others: is the family of concentric circles (orthogonal to radial lines ); represents straight lines; is not an orthogonal family.
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