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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

p^{2} + 2021 = q^{2}

\frac{( y - 1 ) ^{2}}{4 ^{2}} - \frac{( x + 3 ) ^{2}}{5 ^{2}} = 1

x^{2} - 9 y^{2} + 4 x + 18 y - 149 = 3

3 x^{2} - 2 y^{2} - 12 x - 16 y + 4 = 0

4 x^{2} - 5 y^{2} + 32 x + 30 y = 1

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