the Given:
[tex]4x^2+4y^2-8y-117=0[/tex]
Express the equation into standard form,
[tex]\begin{gathered} 4x^2+4y^2-8y-117=0 \\ 4x^2+4y^2-8y=117 \\ x^2+y^2-2y=\frac{117}{4} \\ x^2+y^2-2y+1=\frac{117}{4}+1 \\ (x-0)^2+(y-1)^2=\frac{121}{4} \\ (x-0)^2+(y-1)^2=(\frac{11}{2})^2 \end{gathered}[/tex]
Compare it with standard form of the equation of a circle,
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (h,k)=\text{center} \\ r=\text{radius} \end{gathered}[/tex]
It gives,
Center = (0,1)
Radius = 11/2
