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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( x - 5 ) ^{2}}{25} - \frac{( y + 2 ) ^{2}}{16} = 1

2 x^{2} - 2 y^{2} = 12

\frac{x ^{2}}{9} - \frac{y ^{2}}{14} = 1

\frac{( y + 7 ) ^{2}}{9} - \frac{( x - 5 ) ^{2}}{16} = 1

\frac{x ^{2}}{16} - \frac{y ^{2}}{12} = 1

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