Question

Find the orthogonal trajectories of the family of rectangular hyperbola xy = c².

Answer 1

Given curve is

xy = c² 

x(dy/dx) + y = 0

(dy/dx) = -(y/x)

Replacing dy/dx by – dx/dy, we get

-dx/dy = –y/x

xdx – ydy = 0

2xdx – 2ydy = 0

Integrating, we get 

x² – y² = a²

which is the required orthogonal trajectories.