What is x+y=x^2+y^2 ?

The solution to x+y=x^2+y^2 is Circle with (a,b)=(1/2 , 1/2),r=sqrt(1/2)

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x+y=x^2+y^2

x + y = x^{2} + y^{2}

(a, b) = (\frac{1}{2}, \frac{1}{2}), r = \frac{1}{2}

Solution steps

x + y = x^{2} + y^{2}

Rewrite

x + y = x^{2} + y^{2}

in the form of the standard circle equation

(x - \frac{1}{2})^{2} + (y - \frac{1}{2})^{2} = (\frac{1}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, \frac{1}{2}), r = \frac{1}{2}

(x - 3)^{2} + (y + 4)^{2} = 16

\frac{( y - 2 ) ^{2}}{9} + \frac{( x + \frac{1}{2} ) ^{2}}{9} = 1

4 x^{2} + 4 y^{2} - x + 2 y - 11 = 0

x^{2} + y^{2} - 4 x + 6 y - 12 = 0

x^{2} + y^{2} - 6 x + 2 y + 6 = 0

What is x+y=x^2+y^2 ?
The solution to x+y=x^2+y^2 is Circle with (a,b)=(1/2 , 1/2),r=sqrt(1/2)