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Newton-Raphson Question

  1. Nov 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Really have no idea as to how to proceed:

    Find a point P on the graph of
    x^(2)+y^(2)−62x-12y+828=0
    and a point Q on the graph of
    (y-6)^(2)=x^(3)−56x^(2)−90x+29988
    such that the distance between them is as small as possible.

    To solve this problem, we let (xy) be the coordinates of the point Q. Then we need to minimize the following function of x and y:
    1)_____________________
    After we eliminate y from the above, we reduce to minimizing the following function of x alone:
    2) f(x)=______________
    To find the minimum value of f(x) we need to check the value at the following three points (in increasing order). (You will need to use a numerical method, like Newton-Raphson to find one of these points.)
    3) x1=___________
    4) x2=___________
    5) x3=___________
    We conclude that the minimum value of f(x) occurs at
    6) x=_____________
    Thus a solution to our original question is
    7) P=(____,____)
    8) Q=(____,____)


    3. The attempt at a solution

    I actually thought that the first function in terms of x and y would be (x-31)^2 + (y-6)^2 since minimizing the shortest distance to the circle and minimizing the shortest distance to the centre of the circle are equivalent. But my equation is wrong. How to proceed?
     
  2. jcsd
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