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!

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- Feb 11th 2009, 10:07 PMkhoodorthogonal 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 PMNonCommAlg
differentiate your curve: $\displaystyle x+2yy'=0.$ replace $\displaystyle y'$ with $\displaystyle \frac{-1}{y'}$ to get the differential equation of the orthogonal trajectories: $\displaystyle \frac{y'}{y}=\frac{2}{x}.$ solve the equation to get: $\displaystyle y=cx^2.$