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

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

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

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

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

Solution steps

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

Rewrite

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

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

\frac{1}{144} x^{2} - \frac{1}{196} y^{2} = 1

\frac{x ^{2}}{5 0 ^{2}} - \frac{y ^{2}}{2 5 ^{2}} = 1

81 x^{2} - 64 y^{2} + 1134 x - 640 y - 2815 = 0

\frac{y ^{2}}{3} - \frac{x ^{2}}{16} = 1

2500 x^{2} - 640 x + 41 = y^{2}

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