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Find a point on the parabola with given point and distance

  1. Jan 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Find a point on the parabola y = x^2 whose distance from (18,0) is 4*sqrt(17)


    2. Relevant equations

    I'm guessing I need to use the distance formula, but I'm not entirely sure.
    D = sqrt( (x2 - x1)^2 + (y2 - y1)^2)


    3. The attempt at a solution

    Well I really don't think I'm doing this right. I tried substituting the given point and distance into the equation, but I'm not really sure where to go from there.

    4*sqrt(17) = sqrt( (18 - x)^2 + (0 - y)^2)
    272 = y^2 + x^2 - 36x + 324
    y^2 = -(x-18)^2 + 272

    I'm not really sure what to do. Any help would be greatly appreciated.
     
  2. jcsd
  3. Jan 28, 2012 #2

    tiny-tim

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    welcome to pf!

    hi theintarnets! welcome to pf! :smile:

    that's ok so far …

    now put y2 = x4

    that gives you a quartic equation :yuck: …

    but you should be able to spot one root by guesswork (you only need one :wink:)​
     
  4. Jan 28, 2012 #3
    I'm sorry, I'm not very good at math and I have no idea what you mean.
    So I substitute x^4 for y^2? Can you explain why? And I'm not 100% sure what you mean by finding the roots. I'm so ashamed :cry:
     
  5. Jan 28, 2012 #4
  6. Jan 29, 2012 #5

    tiny-tim

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    hi theintarnets! :smile:

    (just got up :zzz: …)
    hmm … that's a different problem, finding a point at the shortest distance rather than at an actual distance
    this is a standard method for solving a pair of simultaneous equations (ie two equations with two unknowns, x and y) …

    you rewrite one equation to express y in terms of x (or vice versa),

    then you put that value of y into the other equation, giving you an equation with only one unknown (x)! :smile:
    the solutions of a polynomial equation are also known as the roots …

    in this case, there's an obvious whole number that works … try it! :wink:
     
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