# orthogonal trajectory of an ellipse!

• Feb 11th 2009, 10:07 PM
khood
orthogonal trajectory of an ellipse!
Find the orthogonal trajectories of the family of curves.
http://www.webassign.net/www23/symIm...896c31754f.gif

I don't know how to begin this!
• Feb 11th 2009, 11:11 PM
NonCommAlg
Quote:

Originally Posted by khood
Find the orthogonal trajectories of the family of curves.
http://www.webassign.net/www23/symIm...896c31754f.gif

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: $y=cx^2.$