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Math Help - Lines Tangent to a Parabola

  1. #1
    Senior Member topher0805's Avatar
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    Lines Tangent to a Parabola

    Find equations of both lines through the point (2,-3) that are tangent to the parabola y = x^2 + x.

    I know the derivative of the parabola: y' = 2x + 1, but I am not sure how to use that to find the two lines.
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  2. #2
    Eater of Worlds
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    The trick with this is they don't tell you where it's tangent.

    Use y-y_{1}=m(x-x_{1})

    Where y=x^{2}+x, \;\ y_{1}=-3, \;\ m=y'=2x+1, \;\ x_{1}=2

    Then solve for x. You will get two solutions. Those are the x-coordinates of your tangency points.
    Last edited by galactus; November 24th 2008 at 05:38 AM.
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