What is the center x^2-y^2-2x-2y-1=0 ?

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

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center x^2-y^2-2x-2y-1=0

center

x^{2} - y^{2} - 2 x - 2 y - 1 = 0

(1, - 1)

Solution steps

x^{2} - y^{2} - 2 x - 2 y - 1 = 0

Rewrite

x^{2} - y^{2} - 2 x - 2 y - 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

And the center is:

(1, - 1)

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4 x^{2} - 25 y^{2} + 100 y = 200

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4 y^{2} - x^{2} + 24 y + 4 x + 28 = 0