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

The solution to x+2y(y-x)=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(y-x)=2x^2-2xy-x^2

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

Rewrite

x + 2 y (y - x) - 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}

\frac{( x - 6 ) ^{2}}{4} - \frac{( y + 7 ) ^{2}}{36} = 1

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

\frac{( y + 3 ) ^{2}}{( 64 )} - \frac{( x - 2 ) ^{(2)}}{( 84 )} = 1

5 x^{2} - 4 y^{2} - 20 x + 8 y - 4 = 0

\frac{( y - 1 ) ^{2}}{25} - \frac{( x + 2 ) ^{2}}{9} = 1

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