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

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

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

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

(h, k) = (0, - 1), a = \frac{1}{2}, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - ( - 1 ) ) ^{2}}{( \frac{1}{2} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = \frac{1}{2}, b = 2

4 y^{2} - x^{2} = 1

16 y^{2} - 4 x^{2} + 16 x - 80 = 20

x^{2} - y^{2} + 6 x - 4 y + 4 = 0

4 x^{2} - y^{2} + 16 x + 6 y = 9

\frac{x ^{2}}{289} - \frac{( y - 70 ) ^{2}}{1600} = 1

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