What is the family of orthogonal trajectories to the family of rectangular hyperbolas ()?

Answer and explanation

Correct answer: B.

  1. Step 1: Differentiate with respect to : .
  2. Step 2: Replace with to form the differential equation of orthogonal trajectories: .
  3. 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.

Practise more Differential equations.

Free questions with an explanation for every one, and full timed JEE Main mock tests.