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

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

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1=((y-1)^2)/2-(x^2)/2

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

(h, k) = (0, 1), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 1), a = 2, b = 2

x^{2} - y^{2} + 8 y - 12 = 0

4 x^{2} - 5 y^{2} = 20

x^{2} + (x + 3)^{2} = y^{2}

4 x^{2} - 34 y - 5 y^{2} - 36 = 0

(\frac{2 y - 3 x}{18}) (\frac{2 y + 3 x}{2}) = 1

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