What is the center ((y-1)^2)/9-((x-4)^2)/(25)=1 ?

The center ((y-1)^2)/9-((x-4)^2)/(25)=1 is (4,1)

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center ((y-1)^2)/9-((x-4)^2)/(25)=1

center

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 4 ) ^{2}}{25} = 1

(4, 1)

Solution steps

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 4 ) ^{2}}{25} = 1

Rewrite

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 4 ) ^{2}}{25} = 1

in the form of a standard hyperbola equation

\frac{( y - 1 ) ^{2}}{3 ^{2}} - \frac{( x - 4 ) ^{2}}{5 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, 1), a = 3, b = 5

And the center is:

(4, 1)

\frac{( x + 5 ) ^{2}}{\frac{1}{9}} - \frac{( y - 3 ) ^{2}}{\frac{1}{4}} = 1

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

\frac{x ^{2}}{289} - \frac{y ^{2}}{144} = 1

\frac{y ^{2}}{4} - \frac{x ^{2}}{1} = 1

121 - 32 x - 8 x^{2} - 90 y + 9 y^{2} = 0

What is the center ((y-1)^2)/9-((x-4)^2)/(25)=1 ?
The center ((y-1)^2)/9-((x-4)^2)/(25)=1 is (4,1)