# Math Help - orthogonal trajectory of an ellipse!

1. ## orthogonal trajectory of an ellipse!

Find the orthogonal trajectories of the family of curves.

I don't know how to begin this!

2. Originally Posted by khood
Find the orthogonal trajectories of the family of curves.

I don't know how to begin this!
differentiate your curve: $x+2yy'=0.$ replace $y'$ with $\frac{-1}{y'}$ to get the differential equation of the orthogonal trajectories: $\frac{y'}{y}=\frac{2}{x}.$ solve the equation to get: $y=cx^2.$