Orthogonal trajectory for will be (
is parameter)
As we have learnt,
Orthogonal Trajectory -
Any curve which cuts every member of a given family of curves at right angles
- wherein
First of all we need differential equation for given family of curves. So, on differentiating we get -
Now if we replace with
, the resulting equation will be differential equation, for required orthogonal trajectory.
So we get -
Now, Integrating we get -
Option 1)
Option 2)
Option 3)
Option 4)
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