What is the center 9x^2-4y^2-54x-8y+113=0 ?

The center 9x^2-4y^2-54x-8y+113=0 is (3,-1)

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center 9x^2-4y^2-54x-8y+113=0

center

9 x^{2} - 4 y^{2} - 54 x - 8 y + 113 = 0

(3, - 1)

Solution steps

9 x^{2} - 4 y^{2} - 54 x - 8 y + 113 = 0

Rewrite

9 x^{2} - 4 y^{2} - 54 x - 8 y + 113 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 1), a = 3, b = 2

And the center is:

(3, - 1)

9 x^{2} - 4 y^{2} = 36

9 x^{2} - 18 x - 24 y - 63 = 4 y^{2}

\frac{( y + 4 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{25} = 1

\frac{x ^{2}}{25} - \frac{y ^{2}}{9} = 1

\frac{x ^{2}}{49} - \frac{y ^{2}}{16} = 1

What is the center 9x^2-4y^2-54x-8y+113=0 ?
The center 9x^2-4y^2-54x-8y+113=0 is (3,-1)