What is the center x^2-5y^2-6x-10y-1=0 ?

The center x^2-5y^2-6x-10y-1=0 is (3,-1)

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center x^2-5y^2-6x-10y-1=0

center

x^{2} - 5 y^{2} - 6 x - 10 y - 1 = 0

(3, - 1)

Solution steps

x^{2} - 5 y^{2} - 6 x - 10 y - 1 = 0

Rewrite

x^{2} - 5 y^{2} - 6 x - 10 y - 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 1), a = 5, b = 1

And the center is:

(3, - 1)

4 y^{2} = 4 x^{2} + 12 y - 69 + 32 x

4 x^{2} - 12 y^{2} - 24 x + 24 y + 51 = 0

y^{2} - x^{2} = \frac{4}{25}

x^{2} - y^{2} = 15

(x - 5)^{2} - (y - 4)^{2} = 1

What is the center x^2-5y^2-6x-10y-1=0 ?
The center x^2-5y^2-6x-10y-1=0 is (3,-1)