I was looking for a way of graphing the union of two sets and found the following in Desmos - Union of Sets Desmos. I've also included an image Image of Desmos page
My question is what is where has the inquality that defines the region come from?
(e^{-50((x-0.5)^{2}+y^{2}-1)}+e^{-50((x+0.5)^{2}+y^{2}-1)})^{-1}<1
Is it something to do with Euler's equation, hyperbolic functions... or is it just a sort of numerical method. If you recognise it, please could you point me in the right direction of a more general method that lies behind it?
I think that I understand the maths behind it: exponentiating the circle equations, inverse of the complement etc. It's the bit where they are added together that I find confusing. More precisely, it is the power of -50 that I'm intersted in as using -1 instead gives a worse approximation of the area.
I'd be grateful for any help with this and thank you in advance.
MW