Find the orthogonal trajectories of the family 2a/r=1-cos(theta)

Problem

Question

Find the orthogonal trajectories of the family 2a/r=1-cos(theta)

Topic

Applications of Differential Equations

Problems of Differential Equations

  1. Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter
  2. Find the orthogonal trajectories of the family r=a(1+sin(theta))
  3. Find the orthogonal trajectories of the family 2a/r=1-cos(theta)
  4. Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta)
  5. Using the concept of orthogonal trajectories show that the family of curves r=a (sin(theta)+cos(theta)) and r=b (sin(theta)-cos(theta)) intersect each other orthogonally
  6. Show that the family of parabolas y^2=4a (x+a) is self-orthogonal
  7. Find the Orthogonal trajectories of the family r^n cos(n.theta) = a^n

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