What is y^2-2y-(x^2-x-1)=0 ?

The solution to y^2-2y-(x^2-x-1)=0 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)=0

y^{2} - 2 y - (x^{2} - x - 1) = 0

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

Solution steps

y^{2} - 2 y - (x^{2} - x - 1) = 0

Rewrite

y^{2} - 2 y - (x^{2} - x - 1) = 0

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}

4 x^{2} + 4 y^{2} - 9 + 18 y - 9 x^{2} = 0

4 x^{2} + 16 x - 9 y^{2} + 18 y = 29

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

3 y^{2} - x^{2} + 18 y - 4 x + 20 = 0

9 y^{2} - x^{2} = 81

What is y^2-2y-(x^2-x-1)=0 ?
The solution to y^2-2y-(x^2-x-1)=0 is Hyperbola with (h,k)=(1/2 ,1),a= 1/2 ,b= 1/2