orthogonal trajectory of an ellipse!

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February 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!
February 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: $y=cx^2.$

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