What is the center x^2-y^2-8x-2y-19=0 ?

The center x^2-y^2-8x-2y-19=0 is (4,-1)

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center x^2-y^2-8x-2y-19=0

center

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

(4, - 1)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 4 ) ^{2}}{( 34 ) ^{2}} - \frac{( y - ( - 1 ) ) ^{2}}{( 34 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, - 1), a = 34, b = 34

And the center is:

(4, - 1)

\frac{( x - 5 ) ^{2}}{25} - \frac{( y + 4 ) ^{2}}{9} = 1

\frac{( x - 5 ) ^{2}}{7} - \frac{( y + 3 ) ^{2}}{9} = 1

3 x^{2} - 3 y^{2} - 12 x - 6 y + 3 = 0

\frac{( x - 2 ) ^{2}}{36} - \frac{( y + 1 ) ^{2}}{64} = 1

2 y^{2} - 5 x^{2} - 56 y - 90 x - 807 = 0