What is the center x^2-y^2-6x=7 ?

The center x^2-y^2-6x=7 is (3,0)

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center x^2-y^2-6x=7

center

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

(3, 0)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{4 ^{2}} - \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 0), a = 4, b = 4

And the center is:

(3, 0)

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

4 x^{2} - 9 y^{2} - 16 x + 18 y - 11 = 0

\frac{( y - 3 ) ^{2}}{11} - \frac{( x + 1 ) ^{2}}{5} = 1

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

x^{2} - 5 y^{2} - 6 x - 10 y - 1 = 0