What is x^2+y=x+y^2+2018 ?

The solution to x^2+y=x+y^2+2018 is Hyperbola with (h,k)=(1/2 , 1/2),a=sqrt(2018),b=sqrt(2018)

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x^2+y=x+y^2+2018

x^{2} + y = x + y^{2} + 2018

(h, k) = (\frac{1}{2}, \frac{1}{2}), a = 2018, b = 2018

Solution steps

x^{2} + y = x + y^{2} + 2018

Rewrite

x^{2} + y = x + y^{2} + 2018

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{2} ) ^{2}}{( 2018 ) ^{2}} - \frac{( y - \frac{1}{2} ) ^{2}}{( 2018 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, \frac{1}{2}), a = 2018, b = 2018

\frac{( x - 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{16} = 1

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{5} = 1

\frac{( x - 4 ) ^{2}}{36} - \frac{( y + 3 ) ^{2}}{25} = 1

x^{2} - y^{2} = 36

x^{2} - 4 y^{2} + 6 x + 8 y = - 1

What is x^2+y=x+y^2+2018 ?
The solution to x^2+y=x+y^2+2018 is Hyperbola with (h,k)=(1/2 , 1/2),a=sqrt(2018),b=sqrt(2018)