What is the center 4x^2-9y^2-16x+18y-7=0 ?

The center 4x^2-9y^2-16x+18y-7=0 is (2,1)

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

center

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

(2, 1)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{( \frac{7}{2} ) ^{2}} - \frac{( y - 1 ) ^{2}}{( \frac{14}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 1), a = \frac{7}{2}, b = \frac{14}{3}

And the center is:

(2, 1)

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}

\frac{1}{144} x^{2} - \frac{1}{196} y^{2} = 1

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0^{2}

What is the center 4x^2-9y^2-16x+18y-7=0 ?
The center 4x^2-9y^2-16x+18y-7=0 is (2,1)