# Equationsystem problem

 P: 2 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=$\sqrt{b^{2} - (x-f)^{2}}$ + e x=$\sqrt{a^{2} - (y-c)^{2}}$ + d Can anyone help me? And is this equationsystem even possible?
 P: 898 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.
 P: 2 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?
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P: 40,933
Equationsystem problem

 Quote by nastyjoe 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=$\sqrt{b^{2} - (x-f)^{2}}$ + e x=$\sqrt{a^{2} - (y-c)^{2}}$ + d Can anyone help me? And is this equationsystem even possible?
 Quote by nastyjoe 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?
Welcome to the PF.

What are these equations from?
 Engineering Sci Advisor HW Helper Thanks P: 7,112 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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