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If the orthogonal trajectories of the family of circles x2 + y2 = c2, where c is constant, are given by y = kα, where k is constant, then α is (Answer should be integer) _______.
Correct answer is '1'. Can you explain this answer?
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If the orthogonal trajectories of the family of circles x2+ y2= c2, wh...
Differentiating the equations x2 + y2 = c2, we have 2x + 2y dy/dx = 0
To find orthogonal trajectories, we replace dy/dx by dx/dy  then we have 
Integrating both side, we have In y = In x +In k, k is constant.
⇒ y = kx
Now, comparing with y = kxα , we have α  =1
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If the orthogonal trajectories of the family of circles x2+ y2= c2, where c is constant, are given by y = kα,where k is constant, thenα is (Answer should be integer) _______.Correct answer is '1'. Can you explain this answer?
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