Answer:
D
Step-by-step explanation:
Standard equation of the circle is at the origin [tex]x^{2} +y^{2} = r^{2}[/tex] But this is only when the center of the circle is at (0,0). In the quesiton stated the center is (-1/2, √57) .
When the center isn't (0,0) the equation is [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex] (h,k) is center and r is radius.
So inputting the center (-1/2, √57) and radius = in the equation:
[tex](x- -\frac{1}{2} )^{2} + (y-\sqrt{57} )^{2} = 9^{2}[/tex]
[tex](x+\frac{1}{2})^{2} + (y-\sqrt{57} )^{2} = 81[/tex]
