What is the center 9x^2-18x-24y-63=4y^2 ?

The center 9x^2-18x-24y-63=4y^2 is (1,-3)

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center 9x^2-18x-24y-63=4y^2

center

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

(1, - 3)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

And the center is:

(1, - 3)

\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

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305

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

What is the center 9x^2-18x-24y-63=4y^2 ?
The center 9x^2-18x-24y-63=4y^2 is (1,-3)