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Math Help - Question about orthogonal trajectories

  1. #1
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    Question about orthogonal trajectories

    Find the orthogonal trajectories of the family of ellipses

    (x^2/ a^2)+(y^2)=k^2
    where a is a given constant.
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  2. #2
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    Quote Originally Posted by shannon1111 View Post
    Find the orthogonal trajectories of the family of ellipses

    (x^2/ a^2)+(y^2)=k^2
    where a is a given constant.
    For orthogonal trajectories, the tangents to the two respective curve are orthogonal. Slope of the tangent for your ellipse is given by

     <br />
\frac{dy}{dx} = - \frac{x}{a^2 y}<br />

    For the orthogonal trajectory

     <br />
\frac{dy}{dx} = \frac{a^2 y}{x}<br />

    You now have an ODE you can integrate for the actual curve.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    If intersted you may want to see the notes and animations on orthogonal trajectories on the

    differential equations page of http://calculus7.com/
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