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Math Help - Orthogonal Trajectories

  1. #1
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    Orthogonal Trajectories

    I'm confused as to how to do orthogonal trajectory problems. The current calculus book I have doesn't explain how to do these problems, yet these problems appear in the back of some of the chapters in the book.

    Here's an example problem:

    Find the value of the number a such that the families of curves y=(x+c)^{-1} and y=a(x+k)^{1/3} are orthogonal trajectories.

    How would I go about doing this?
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  2. #2
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    Orthogonal trajectories are families of curves that intersect at right angles. This must mean that the product of their respective derivatives is -1.

    Let's see what you get.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    Orthogonal trajectories are families of curves that intersect at right angles. This must mean that the product of their respective derivatives is -1.

    Let's see what you get.
    I think it must be "...the product of their respective derivatives at their intersection point is -1"

    Tonio
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  4. #4
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    One related question:
    Since they're orthogonal then it means that y' of the first is (m) and y' of the other is (-1/m) at their point of intersection right?
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  5. #5
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    Well, for m NOT = zero (0), m*(-1/m) = -1
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