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Intersection of a parabola with another curve

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data
    For a any parabola with the equation [tex]y=kx^{2}[/tex]
    I'm trying to find a curve that intersect every point of the parabola at right angles.


    2. Relevant equations

    For a perpendicular intersection the slope is [tex]-\frac{1}{m}[/tex]


    3. The attempt at a solution

    I took the derivative and then took the negative reciprocal of the derivative.

    [tex]\frac{dy}{dx} = -\frac{1}{2kx}[/tex]

    Then I isolated the variables on different sides and then integrated. I ended up with:

    [tex]y+ \frac{1}{2k}*ln(|x|) = 0 [/tex]

    My problem is when I graph the two functions there is only one intersection and I was wondering if there was any flaws in my logic I used to reach my answer.
     
  2. jcsd
  3. Sep 27, 2009 #2
    Don't forget that you get a constant +C when you integrate.

    so

    [tex]
    y+ \frac{1}{2k}*ln(|x|) = 0
    [/tex]

    would actually be

    [tex]
    y+ \frac{1}{2k}*ln(|x|) = C
    [/tex]
     
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