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

The solution to y^2-2y=x^2-x is Hyperbola with (h,k)=(1/2 ,1),a=(sqrt(3))/2 ,b=(sqrt(3))/2

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

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

(h, k) = (\frac{1}{2}, 1), a = \frac{3}{2}, b = \frac{3}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, 1), a = \frac{3}{2}, b = \frac{3}{2}

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

x^{2} - 8 y^{2} = 64

4 x^{2} - 12 y^{2} + 8 x - 2 y = 2

(\frac{x - 3}{16})^{2} - (\frac{y + 2}{36})^{2} = 1

y^{2} = x^{2} + 16

What is y^2-2y=x^2-x ?
The solution to y^2-2y=x^2-x is Hyperbola with (h,k)=(1/2 ,1),a=(sqrt(3))/2 ,b=(sqrt(3))/2