What is y^2-2x^2+4x-4y=0 ?

The solution to y^2-2x^2+4x-4y=0 is Hyperbola with (h,k)=(1,2),a=sqrt(2),b=1

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y^2-2x^2+4x-4y=0

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

(h, k) = (1, 2), a = 2, b = 1

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 2), a = 2, b = 1

9 x^{(2)} - 36 x - 16 y^{(2)} - 32 y = 124

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

4 x^{2} - 24 x - 36 y^{2} - 360 y + 864 = 0

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

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

What is y^2-2x^2+4x-4y=0 ?
The solution to y^2-2x^2+4x-4y=0 is Hyperbola with (h,k)=(1,2),a=sqrt(2),b=1