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Math Help - Tangent Lines, Parallel Lines, and Normal Lines

  1. #1
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    Question Tangent Lines, Parallel Lines, and Normal Lines

    Find an equation of each line normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Pretty sure it would just be y = 2x

    It runs parallel to y=2x + 1 and would be perpendicular to the tangent lines at those points.

    Are you supposed to find one line that will apply to both graphs?
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  3. #3
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    Quote Originally Posted by kinana18 View Post
    Find an equation of each line normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0
    y = \frac{2x}{x - 1} = 2 + \frac{2}{x-1} \Rightarrow \frac{dy}{dx} = \frac{-2}{(x-1)^2}.

    You want the normal to be parallel to 2x - y + 1 = 0 \Rightarrow y = 2x + 1.

    To find the x-coordinates of the required normal solve \frac{(x-1)^2}{2} = 2: x = 0, 2.

    Therefore the required normal is normal to the curve at (0, 0) and (2, 4). The equation of this normal is y = 2x.

    Note: The normal is also the line of symmetry of the curve.
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