# Equationsystem problem

1. ### nastyjoe

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?

2. ### slider142

958
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.

3. ### nastyjoe

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?

### Staff: Mentor

Welcome to the PF.

What are these equations from?

5. ### AlephZero

7,300
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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