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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 20 x - 4 y^{2} - 64 y - 172 = 0

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

x^{2} + (y - 5) = (y + 5)^{2}

2 x^{2} - 4 y^{2} = 3

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

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