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

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

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

center

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

(3, - 2)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

And the center is:

(3, - 2)

x^{2} - y^{2} = 6

x^{2} - 25 y^{2} - 14 x + 100 y - 76 = 0

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

\frac{x ^{2}}{100} - \frac{y ^{2}}{64} = 1

9 y^{2} - 25 x^{2} - 100 x - 108 y - 1 = 0

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