What is the center 9=2y-y^2-6*(-x^2) ?

The center 9=2y-y^2-6*(-x^2) is (0,1)

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center 9=2y-y^2-6*(-x^2)

center

9 = 2 y - y^{2} - 6 \cdot (- x^{2})

(0, 1)

Solution steps

9 = 2 y - y^{2} - 6 (- x^{2})

Rewrite

9 - 2 y + y^{2} + 6 (- x^{2}) = 0

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{2}{3} ) ^{2}} - \frac{( y - 1 ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 1), a = \frac{2}{3}, b = 22

And the center is:

(0, 1)

4 x^{2} + 9 y^{2} + 3 x - 18 y^{2} + 37 = 0

9 y^{2} - x^{2} - 36 y - 6 x + 18 = 0

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

\frac{( y - ( - 2 ) ) ^{2}}{9} - \frac{( x - 5 ) ^{2}}{27} = 1

\frac{( y - 2 ) ^{2}}{14} - \frac{( x + 6 ) ^{2}}{3} = 4