What is 2x^2-2y^2-2x+4y= 1/2 ?

The solution to 2x^2-2y^2-2x+4y= 1/2 is Hyperbola with (h,k)=(1/2 ,1),a=sqrt(1/2),b=sqrt(1/2)

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2x^2-2y^2-2x+4y= 1/2

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - x - 4 y^{2} + 24 y - 35 = 0

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

y^{2} = x^{2} + 12

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

x^{2} \frac{1}{4} - y^{2} \frac{1}{9} = 1

What is 2x^2-2y^2-2x+4y= 1/2 ?
The solution to 2x^2-2y^2-2x+4y= 1/2 is Hyperbola with (h,k)=(1/2 ,1),a=sqrt(1/2),b=sqrt(1/2)