What is 4x^{(2)}-4y^{(2)}-4x+8y-19=0 ?

The solution to 4x^{(2)}-4y^{(2)}-4x+8y-19=0 is Hyperbola with (h,k)=(1/2 ,1),a=2,b=2

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4x^{(2)}-4y^{(2)}-4x+8y-19=0

4 x^{(2)} - 4 y^{(2)} - 4 x + 8 y - 19 = 0

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

Solution steps

4 x^{2} - 4 y^{2} - 4 x + 8 y - 19 = 0

Rewrite

4 x^{2} - 4 y^{2} - 4 x + 8 y - 19 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

- \frac{y ^{2}}{4} + \frac{z ^{2}}{9} = 1

10 x^{2} - 64 y^{2} - 140 x + 768 y - 2454 = 0

y^{2} - 16 x^{2} = 1

\frac{( y - 3 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1

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

What is 4x^{(2)}-4y^{(2)}-4x+8y-19=0 ?
The solution to 4x^{(2)}-4y^{(2)}-4x+8y-19=0 is Hyperbola with (h,k)=(1/2 ,1),a=2,b=2