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Math Help - Testing for the focus of a parabola using equations of normals: what did I do wrong?

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    Testing for the focus of a parabola using equations of normals: what did I do wrong?

    I'm trying to prove that the focus of the equation to the parabola y^2=x is at (.25,0); for y^2=x, the "p" value is .25. My hypothesis is that all normals of the lines tangent to each ordered pair for the equation y^2=x intersect at the focus.

    I used 3 points on y^2=x to demonstrate this; Points A,B,C, [(1,1),(4,2),(9,3)] respectively.
    I used the first derivative function to find the slops at each point: y'(x) = (.5)x^(-.5)
    @ A: Slope = .5
    @ B: Slope = .25
    @ C: Slope = 15/90
    Tangent Lines through A,B,C are (respectively):
    y = .5x + .5
    y = .25x +1
    y = (15/90)x + 1.5
    The corresponding equations for the normals are (respectively):
    y = -2x+3
    y = -4x+18
    y = -6x+27

    The parabola opens to the right and has the focus located at (.25,0). If my hypothesis and calculations are done correctly, all 3 normal equations should intersect at the focus. Thus (.25,0) should be the ordered pair for all three equations of the normals. But it isn't.


    [Solved: No connection between parabolic reflection and normals]
    Last edited by Masterthief1324; February 25th 2011 at 11:49 PM. Reason: Solved
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