What is x^2-2x+1=2k(x)(k(x)-2) ?

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

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x^2-2x+1=2k(x)(k(x)-2)

x^{2} - 2 x + 1 = 2 k (x) (k (x) - 2)

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

16 x^{2} - 25 y^{2} = 100

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

4 x^{2} - 4 y^{2} - 16 = 0

\frac{x ^{2}}{25} - \frac{y ^{2}}{25} = 1

\frac{x ^{2}}{16} - \frac{y ^{2}}{16} = 1

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