What is the center 9y^2-x^2-36y-6x+18=0 ?

The center 9y^2-x^2-36y-6x+18=0 is (-3,2)

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center 9y^2-x^2-36y-6x+18=0

center

9 y^{2} - x^{2} - 36 y - 6 x + 18 = 0

(- 3, 2)

Solution steps

9 y^{2} - x^{2} - 36 y - 6 x + 18 = 0

Rewrite

9 y^{2} - x^{2} - 36 y - 6 x + 18 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

And the center is:

(- 3, 2)

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

\frac{( y - ( - 2 ) ) ^{2}}{9} - \frac{( x - 5 ) ^{2}}{27} = 1

\frac{( y - 2 ) ^{2}}{14} - \frac{( x + 6 ) ^{2}}{3} = 4

4 x^{2} - 8 y^{2} = 3

4 x^{2} - 6 x + 2 = y^{2} - 10 y

What is the center 9y^2-x^2-36y-6x+18=0 ?
The center 9y^2-x^2-36y-6x+18=0 is (-3,2)