What is the center x^2-6x-6=y^2+6y+6 ?

The center x^2-6x-6=y^2+6y+6 is (3,-3)

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center x^2-6x-6=y^2+6y+6

center

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

(3, - 3)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 3), a = 23, b = 23

And the center is:

(3, - 3)

y^{2} - 4 y - 4 x^{2} + 13 = 0

\frac{( y + 3 ) ^{2}}{4} - \frac{( x + 1 ) ^{2}}{16} = 1

\frac{( x - 1 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{16} = 1

x^{2} - y^{2} = 9

4 y^{2} - 9 x^{2} + 16 y + 18 x = 29