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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

\frac{1}{144} x^{2} - \frac{1}{196} y^{2} = 1

\frac{x ^{2}}{5 0 ^{2}} - \frac{y ^{2}}{2 5 ^{2}} = 1

81 x^{2} - 64 y^{2} + 1134 x - 640 y - 2815 = 0

\frac{y ^{2}}{3} - \frac{x ^{2}}{16} = 1

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