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

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

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x^2-2y^2=2x

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

(h, k) = (1, 0), a = 1, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 0), a = 1, b = \frac{1}{2}

4 x^{2} - 25 (y - 1)^{2} = 100

\frac{x ^{2}}{- 5} - \frac{y ^{2}}{- 5} = 1

16 x^{2} - y^{2} - 32 x - 6 y - 57 = 0

\frac{y ^{2}}{25} - \frac{( x + 1 ) ^{2}}{16} = 1

6 x^{2} - 5 y^{2} + 36 x + 20 y - 16 = 0

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