What is the center ((y-(-2))^2)/9-((x-5)^2)/(27)=1 ?

The center ((y-(-2))^2)/9-((x-5)^2)/(27)=1 is (5,-2)

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center ((y-(-2))^2)/9-((x-5)^2)/(27)=1

center

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

(5, - 2)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (5, - 2), a = 3, b = 33

And the center is:

(5, - 2)

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

4 x^{2} - 8 y^{2} = 3

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

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

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

What is the center ((y-(-2))^2)/9-((x-5)^2)/(27)=1 ?
The center ((y-(-2))^2)/9-((x-5)^2)/(27)=1 is (5,-2)