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

The center x^2-(y-4)^2=1 is (0,4)

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center x^2-(y-4)^2=1

center

x^{2} - (y - 4)^{2} = 1

(0, 4)

Solution steps

x^{2} - (y - 4)^{2} = 1

Rewrite

x^{2} - (y - 4)^{2} = 1

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{1 ^{2}} - \frac{( y - 4 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 4), a = 1, b = 1

And the center is:

(0, 4)

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

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

\frac{( y - 5 ) ^{2}}{16} - \frac{( x - 4 ) ^{2}}{64} = 1

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

y^{2} - x^{2} = 1