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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - (y - 1)^{2} = 4

x^{2} - y^{2} + 6 x - 4 y - 4 = 0

\frac{y ^{2}}{16} - \frac{x ^{2}}{36} = 1

16 x^{2} - 9 y^{2} - 96 x + 288 = 0

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

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