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

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

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

center

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

(- 2, \frac{1}{2})

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, \frac{1}{2}), a = 2, b = 2

And the center is:

(- 2, \frac{1}{2})

- 9 x^{2} + y^{2} - 72 x - 153 = 0

\frac{( x - 3 ) ^{2}}{8 ^{2}} - \frac{( y - 2 ) ^{2}}{8 ^{2}} = 1

\frac{( x + 2 ) ^{2}}{36} - \frac{( y - 3 ) ^{2}}{16} = 1

x^{2} - y^{2} - 6 x = 7

4 y^{2} - x^{2} = 900

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