What is the center (x^2)/6-(y^2)/8 =1 ?

The center (x^2)/6-(y^2)/8 =1 is (0,0)

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center (x^2)/6-(y^2)/8 =1

center

\frac{x ^{2}}{6} - \frac{y ^{2}}{8} = 1

(0, 0)

Solution steps

\frac{x ^{2}}{6} - \frac{y ^{2}}{8} = 1

Rewrite

\frac{x ^{2}}{6} - \frac{y ^{2}}{8} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 6, b = 22

And the center is:

(0, 0)

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

4 x^{2} - 3 y^{2} - 8 x - 8 = 0

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

x^{2} - y^{2} + 7 x + 8 y = 5

\frac{( x - 4 ) ^{2}}{36} - \frac{( y - 2 ) ^{2}}{9} = 1