What is x^2-2x-y^2+2y=1 ?

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

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x^2-2x-y^2+2y=1

x^{2} - 2 x - y^{2} + 2 y = 1

(h, k) = (1, 1), a = 1, b = 1

Solution steps

x^{2} - 2 x - y^{2} + 2 y = 1

Rewrite

x^{2} - 2 x - y^{2} + 2 y = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 1), a = 1, b = 1

4 x^{2} - y^{2} = 1

16 x^{2} - 9 y^{2} = 1

x^{2} - y^{2} - 6 x = 7

y^{2} = 4 + x^{2}

\frac{( x + 1 ) ^{2}}{9} - \frac{( y - 4 ) ^{2}}{49} = 1

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