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

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

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

center

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

(2, - 3)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

And the center is:

(2, - 3)

\frac{x ^{2}}{9} - \frac{y ^{2}}{16} = 1

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{4} = 1

\frac{x ^{2}}{4} - \frac{y ^{2}}{25} = 1

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

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