The center of the hyperbola whose equation is as given in the complete question is; (6, -3).
The equation of a parabola usually takes the form;
[tex]\frac{(y-h)^{2} }{b} - \frac{(x-g)^{2} }{a} = 1[/tex]
In this scenario, the coordinates of the center the hyperbola is given as; (g, h).
According to the complete version of the task content, the equation of the hyperbola whose center is required is;
[tex]\frac{(y+3)^{2} }{81} - \frac{(x-6)^{2} }{89} = 1[/tex]
On this note, it therefore follows that the center of the hyperbola given by the equation above is; (6, -3).
Remarks:
The equation of the parabola given in the complete task content is;
[tex]\frac{(y+3)^{2} }{81} - \frac{(x-6)^{2} }{89} = 1[/tex]
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