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

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

x^{2} - 9 y^{2} + 4 x + 18 y - 149 = 0

4 y^{2} - 24 y - 2 x^{2} + 20 x = 22

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

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

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