What is the center 9x^2-16y^2-36x+96y+252=0 ?

The center 9x^2-16y^2-36x+96y+252=0 is (2,3)

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center 9x^2-16y^2-36x+96y+252=0

center

9 x^{2} - 16 y^{2} - 36 x + 96 y + 252 = 0

(2, 3)

Solution steps

9 x^{2} - 16 y^{2} - 36 x + 96 y + 252 = 0

Rewrite

9 x^{2} - 16 y^{2} - 36 x + 96 y + 252 = 0

in the form of a standard hyperbola equation

\frac{( y - 3 ) ^{2}}{( \frac{3 5}{2} ) ^{2}} - \frac{( x - 2 ) ^{2}}{( 2 10 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 3), a = \frac{3 5}{2}, b = 210

And the center is:

(2, 3)

5 y^{2} - 16 x^{2} + 400 = 0

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

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

\frac{( y - 1 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{16} = 1

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

What is the center 9x^2-16y^2-36x+96y+252=0 ?
The center 9x^2-16y^2-36x+96y+252=0 is (2,3)