Question

The orthogonal trajectories of the cardioids \[ r=a(1-\cos\theta) \] is:

• A. \(r=a(1+\sin\theta)\)
• B. \(r=a(1-\sin\theta)\)
• C. \(r=a(1+\cos\theta)\)
• D. \(r=a\cos\theta\)

Hint:

For polar orthogonal trajectories, convert the given family into a differential equation and replace the slope by the perpendicular slope.

Answer 1

The Correct Option is C