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

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

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

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

(h, k) = (- 4, - 1), a = 2, b = 1

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 4, - 1), a = 2, b = 1

4 x^{2} - 25 y^{2} - 40 x - 150 y - 225 = 0

4 x^{2} - 5 y^{2} - 32 x + 10 y + 79 = 0

(x + k (x)) (x - k (x)) = k (x)

\frac{x ^{2}}{16} - \frac{y ^{2}}{64} = 1

\frac{x ^{2}}{81} - \frac{y ^{2}}{64} = 1

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