What is the center 9x^2-36x-4y^2-24y-36=0 ?

The center 9x^2-36x-4y^2-24y-36=0 is (2,-3)

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center 9x^2-36x-4y^2-24y-36=0

center

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

(2, - 3)

Solution steps

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

Rewrite

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

And the center is:

(2, - 3)

4 x^{2} - y^{2} = 16

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

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

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

x^{2} - y^{2} = 10 (x - y) + 1

What is the center 9x^2-36x-4y^2-24y-36=0 ?
The center 9x^2-36x-4y^2-24y-36=0 is (2,-3)