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Math Help - Geometric problem

  1. #1
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    Geometric problem

    Hi there. I have this exercise in my practice for differential equations, and it asks me to find the curve that satisfice for every point (on the xy plane) the distance from every point (x,y) over the curve to the points of intersection for the tangent line and the x axis, and the normal with the x axis remains constant

    So I stated it this way, I don't know if it's right:

    I called x1 to the point of intersection for the normal line and the x axis :
    \displaystyle\frac{-1}{y'}(x_1-x)+y=0\Rightarrow{x_1=yy'+x}

    And x2 to the point of intersection for the tangent line and the x axis:
    y'(x_2-x)+y=0\Rightarrow{x_2=\displaystyle\frac{-y}{y'}+x}

    Then I stated this differential equation, which is the sum of the distances from the (x,y) point on the curve to the intersections on the normal and the tangent line for that point of the curve and the x axis.
    \sqrt[ ]{y^2+(yy')^2}+\sqrt[ ]{y^2+ \left ( \displaystyle\frac{y}{y'} \right )^2}=C

    I'm not sure if this is right, and I don't know how to solve this diff. equation.

    Bye there, and thanks for your help in advance
    Last edited by Ulysses; August 11th 2011 at 05:01 PM. Reason: Correction
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  2. #2
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    Re: Geometric problem

    I've made a correction, the problem statement wasn't clear.
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