Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Orthogonal Trajectory?

find the orthogonal trajectories of the family of curves given by

the equation

y = k / x

where k is an arbitrary constant

Could you please show working:)


3 Answers

  • Anonymous
    1 decade ago
    Favorite Answer

    I don't know how much this is going to help, but to start, you can base your answer off the fact that this is a direct variation equation. This basically means that with k as a constant, y varies directly with x. In other words, if the constant is positive, you will have a constantly positive slope, but if the constant is negative, you will have a consistently negative slope.

    With that said, I'm not sure how much information is needed for the family of curves you want.

  • qwert
    Lv 5
    1 decade ago

    first find the diff. equation of the given family, then replace y' with (-1/y' ) to get the diff.equation of the orthogonal trajectory, then solve the resultant diff. equation

    see this page for more details

  • 5 years ago

    Hi, just wanted to mention, I loved this discussion. quite inspiring replies

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