Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta)

## Problem

## Question

Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta)

## Topic

Applications of Differential Equations

## Problems of Differential Equations

- Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter
- Find the orthogonal trajectories of the family r=a(1+sin(theta))
- Find the orthogonal trajectories of the family 2a/r=1-cos(theta)
- Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta)
- 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
- Show that the family of parabolas y^2=4a (x+a) is self-orthogonal
- Find the Orthogonal trajectories of the family r^n cos(n.theta) = a^n