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

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

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

center

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

(- 3, - 1)

Solution steps

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

Rewrite

4 y^{2} - 9 x^{2} + 8 y - 54 x - 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)

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

9 x^{2} - 16 y^{2} - 108 x + 128 y + 212 = 0

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

x^{2} - y^{2} - 4 x - 2 y - 1 = 0

x^{2} - y^{2} = 49

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