User:TenBillionPlusOne/Sandbox

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Behaviour of equation

Equation x^2+y^2−a = √x+a^x has interesting properties.

For a<0, no point satisfies it.
For 0<=a<=1, the points that satisfy it form a single, finite curve.
For 1<a<ϱ, the points that satisfy it for two curves - one finite and one infinite.
For ϱ<a, the points that satisfy it form a single, infinite curve.

1.86657<ϱ<1.86658