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Thread: Finding equation of a line

  1. #1
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    Talking Finding equation of a line

    i don't understand this AT ALL. oh calculus.
    would it be 10x-5, while 10 is the slope...gah i have no clue X_X plz help



    Find an equation of the line that is both normal to the given parabola and also parallel to the given line

    y = 5 x 2 - 5 x + 6
    x -
    5 y = 6
    Last edited by mr fantastic; Sep 27th 2009 at 02:33 AM. Reason: Improved post title, removed excessive smilies.
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  2. #2
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    $\displaystyle y = 5x^2 - 5x + 6 $

    $\displaystyle y' = 10x - 5 $

    the gradient function is 10x - 5.

    the line
    $\displaystyle x - 5y = 6 $
    $\displaystyle x - 6 = 5y $
    $\displaystyle \frac{x}{5}- \frac{6}{5} = y$

    the gradient of the wanted line must be 6/5, and hence 6/5 is the normal to the parabola. the gradient of the tangent to the parabola must therefore be -5/6

    $\displaystyle \frac{-5}{6}= 10x - 5 $

    Solve for x

    $\displaystyle 4\tfrac{1}{6} = 10x$

    $\displaystyle x= \frac{5}{12} $

    when $\displaystyle x= \frac{5}{12} $ $\displaystyle y = 4\tfrac{113}{144} $

    Equation of the line

    $\displaystyle \frac{y - 4\tfrac{113}{144}}{x - \frac{5}{12}} = \frac{6}{5} $

    cross multiply and you get your answer (i think)
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