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

The solution to 2x^2-2y=2y^2+2y+2x-1 is Hyperbola with (h,k)=(1/2 ,-1),a=(sqrt(5))/2 ,b=(sqrt(5))/2

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

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

(h, k) = (\frac{1}{2}, - 1), a = \frac{5}{2}, b = \frac{5}{2}

Solution steps

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

Rewrite

2 x^{2} - 2 y - 2 y^{2} - 2 y - 2 x + 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, - 1), a = \frac{5}{2}, b = \frac{5}{2}

(\frac{x - 8}{3})^{2} - (\frac{y + 3}{4})^{2} = 1

\frac{y ^{2}}{20} - x^{2} = 1

9 x^{2} - 4 y^{2} - 36 x + 72 = 0

\frac{z ^{2}}{4} - y^{2} = 1

\frac{( y + 5 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{25} = 9

What is 2x^2-2y=2y^2+2y+2x-1 ?
The solution to 2x^2-2y=2y^2+2y+2x-1 is Hyperbola with (h,k)=(1/2 ,-1),a=(sqrt(5))/2 ,b=(sqrt(5))/2