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Math Help - Orthogonal Trajectories

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    Orthogonal Trajectories

    I need some quick homework help with a calculus problem. The problem is as follows:

    Find the orthogonal trajectories of the family of curves:

    (x^2)+(2y^2)=18k^2 where k is any real number.

    Help please!!!!
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  2. #2
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    Quote Originally Posted by Jessica098 View Post
    I need some quick homework help with a calculus problem. The problem is as follows:

    Find the orthogonal trajectories of the family of curves:

    (x^2)+(2y^2)=18k^2 where k is any real number.

    Help please!!!!
    I assume you know the definition of an orthogonal trajectory.

    Using implicit differentiation: 2x + 4y \, \frac{dy}{dx} = 0 \Rightarrow \frac{dy}{dx} = - \frac{x}{2y}.

    So the orthogonal trajectories are the family of curves given by the solutions to the differential equation \frac{dy}{dx} = \frac{2y}{x} .......
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