What is 2x^2-4y^2-4x-8y=6 ?

The solution to 2x^2-4y^2-4x-8y=6 is Hyperbola with (h,k)=(1,-1),a=sqrt(2),b=1

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2x^2-4y^2-4x-8y=6

2 x^{2} - 4 y^{2} - 4 x - 8 y = 6

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

Solution steps

2 x^{2} - 4 y^{2} - 4 x - 8 y = 6

Rewrite

2 x^{2} - 4 y^{2} - 4 x - 8 y = 6

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( x + 1 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{12} = 1

4 x^{2} - 45 y^{2} = 180

- \frac{x ^{2}}{5} + \frac{y ^{2}}{7} = 1

x^{2} - y^{2} + 2 x + 4 y - 12 = 0

\frac{x ^{2}}{36} - \frac{y ^{2}}{13} = 1

What is 2x^2-4y^2-4x-8y=6 ?
The solution to 2x^2-4y^2-4x-8y=6 is Hyperbola with (h,k)=(1,-1),a=sqrt(2),b=1