Equationsystem problem

  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. 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. 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. berkeman

    Staff: Mentor

    Welcome to the PF.

    What are these equations from?
  6. AlephZero

    AlephZero 7,298
    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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