What is the center x^2-y^2+2y=0 ?

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

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center x^2-y^2+2y=0

center

x^{2} - y^{2} + 2 y = 0

(0, 1)

Solution steps

x^{2} - y^{2} + 2 y = 0

Rewrite

x^{2} - y^{2} + 2 y = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

And the center is:

(0, 1)

25 y^{2} - 16 x^{2} - 400 = 0

9 x^{2} - 16 y^{2} = 144

\frac{( x + 1 ) ^{2}}{25} - \frac{( y - 4 ) ^{2}}{144} = 1

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

+ \frac{x ^{2}}{49} - \frac{y ^{2}}{9} = 1