What is the center 2x^2-y^2-2y=-5 ?

The center 2x^2-y^2-2y=-5 is (0,-1)

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center 2x^2-y^2-2y=-5

center

2 x^{2} - y^{2} - 2 y = - 5

(0, - 1)

Solution steps

2 x^{2} - y^{2} - 2 y = - 5

Rewrite

2 x^{2} - y^{2} - 2 y = - 5

in the form of a standard hyperbola equation

\frac{( y - ( - 1 ) ) ^{2}}{( 6 ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 6, b = 3

And the center is:

(0, - 1)

- 6 x^{2} + 4 y^{2} + 6 x + 16 y - 1 = 0

y^{2} - 4 x^{2} < 1

- 9 x^{2} + 8 y^{2} + 36 x + 48 y = 36

\frac{y ^{2}}{36} - \frac{x ^{2}}{16} = 1

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