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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

16 x^{2} - y^{2} - 96 x - 6 y + 119 = 0

\frac{x ^{2}}{40} - \frac{y ^{2}}{120} = 1

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

9 x^{2} - 16 y^{2} - 36 x - 96 y - 252 = 0

y^{2} = 4 x^{2} - 9

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