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Equation of a curve

  1. Dec 8, 2008 #1
    Can anyone help as it's a long time since I studied this:

    I have a straight line - which I have the equation for and a plotted curve with multiple points.

    I want to figure out the point where the curve would touch the line shold it be moved toward the line.

    I've tried using excel to get the equation of the line for the curve but it won't seem to select all the points and is not giving me a good equation.

    Any advice apprecaited!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 8, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If you were to move the line to the curve, or the curve to the line (I presume you mean moving it "parallel to itself", without changing its orientation), they would first touch at a point at which the line is tangent to the curve.

    So: determine the slope of the line. Differentiate the function determining the curve and set the derivative (slope of the tangent line), as a function of x, equal to the slope of the given line. Solve that equation for x.
     
  4. Dec 8, 2008 #3
    Thanks.

    Suppose we were to imagine that I'm a bit rusty with this can I ask a further question?

    What is the best way for me to derive the equation of the curve?

    If I give the simple details it may help.

    Straight Line Equation
    Y = 1022.7X + 115583 (I think!)
    Points
    9.0, 129150
    11.0, 134000

    Curve Points
    29.6 77023
    29.6 78363
    29.6 79033
    29.6 79703
    29.6 80373
    29.7 81043
    29.7 81713
    29.8 82383
    29.9 83053
    30.0 83723
    30.2 84393
    30.4 85063
    30.7 85733
    31.0 86403
    31.3 87073
    31.7 87743
    32.2 88413
    32.8 89083
    33.4 89753
    34.1 90423
    34.9 91093
    35.7 91763
    36.7 92433
    37.7 93103
    38.9 93773
    39.9 94282

    Any advice appreciated!
     
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