What is the center 9x^2-4y^2+54x-8y+78=0 ?

The center 9x^2-4y^2+54x-8y+78=0 is (-3,-1)

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center 9x^2-4y^2+54x-8y+78=0

center

9 x^{2} - 4 y^{2} + 54 x - 8 y + 78 = 0

(- 3, - 1)

Solution steps

9 x^{2} - 4 y^{2} + 54 x - 8 y + 78 = 0

Rewrite

9 x^{2} - 4 y^{2} + 54 x - 8 y + 78 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, - 1), a = \frac{1}{2}, b = \frac{1}{3}

And the center is:

(- 3, - 1)

\frac{x ^{2}}{4} - \frac{y ^{2}}{12} = 1

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

- 321 + 108 x - 9 x^{2} + 8 y + 4 y^{2} = 0

\frac{( y - 5 ) ^{2}}{81} - \frac{( x + 8 ) ^{2}}{9} = 1

\frac{x ^{2}}{64} - \frac{y ^{2}}{36} = 1

What is the center 9x^2-4y^2+54x-8y+78=0 ?
The center 9x^2-4y^2+54x-8y+78=0 is (-3,-1)