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Equationsystem problem

  1. Mar 20, 2013 #1
    My maths skills are so rusty that I can't figure out how I simplify these equations so that I get a formula for x and y... a,b,c,d,e,f are constants

    y=[itex]\sqrt{b^{2} - (x-f)^{2}}[/itex] + e
    x=[itex]\sqrt{a^{2} - (y-c)^{2}}[/itex] + d

    Can anyone help me? And is this equationsystem even possible?
  2. jcsd
  3. Mar 20, 2013 #2
    If you subtract the constants from both sides and square both sides, you should be able to see that your equations can be graphed in the xy-plane as the upper hemisphere of a circle of radius b centered at (f, e) and the upper hemisphere of a circle of radius a centered at (d, c). Whether these two curve segments intersect or not is up to the values of the constants.
    To start, you can just use substitution: substitute your expression for y as a function of x into the second equation.
  4. Mar 20, 2013 #3
    I tried substituting y as a function of x into the second equation but I got an awfully complicated equation which I was unable to solve as I'm not that good at maths... :( Are you able to get a solution?
  5. Mar 20, 2013 #4


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    Staff: Mentor

    Welcome to the PF.

    What are these equations from?
  6. Mar 20, 2013 #5


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    Science Advisor
    Homework Helper

    If you square the first equation, you get
    ##(y-e)^2 + (x-f)^2 = b^2##

    If you draw a graph of that equation, what shape of curve do you get? (If you can't see the answer to that, start with the simpler case when e = f = 0).

    The easiest way to solve the two equations is using geometry, not algebra.
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