What is y^2-4x^2-4y-8x-4=0 ?

The solution to y^2-4x^2-4y-8x-4=0 is Hyperbola with (h,k)=(-1,2),a=2,b=1

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y^2-4x^2-4y-8x-4=0

y^{2} - 4 x^{2} - 4 y - 8 x - 4 = 0

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

Solution steps

y^{2} - 4 x^{2} - 4 y - 8 x - 4 = 0

Rewrite

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

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

x^{2} - y^{2} + 8 y - 12 = 0

4 x^{2} - 5 y^{2} = 20

x^{2} + (x + 3)^{2} = y^{2}

4 x^{2} - 34 y - 5 y^{2} - 36 = 0

What is y^2-4x^2-4y-8x-4=0 ?
The solution to y^2-4x^2-4y-8x-4=0 is Hyperbola with (h,k)=(-1,2),a=2,b=1