What is the center-9x^2+y^2-72x-153=0 ?

The center-9x^2+y^2-72x-153=0 is (-4,0)

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center-9x^2+y^2-72x-153=0

center

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

(- 4, 0)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 4, 0), a = 3, b = 1

And the center is:

(- 4, 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

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