[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h,k) - the center
r - the radius
[tex]4x^2+4y^2+4x-16y-19=0 \ \ \ |\div 4 \\
x^2+y^2+x-4y-\frac{19}{4}=0 \\
x^2+x+\frac{1}{4}+y^2-4y+4-\frac{19}{4}-\frac{1}{4}-4=0 \\
(x+\frac{1}{2})^2+(y-2)^2-\frac{20}{4}-4=0 \\
(x+\frac{1}{2})^2+(y-2)^2-5-4=0 \\
(x+\frac{1}{2})^2+(y-2)^2-9=0 \\
(x+\frac{1}{2})^2+(y-2)^2=9 \\
(x+\frac{1}{2})^2+(y-2)^2=3^2[/tex]
The center - [tex](-\frac{1}{2},2)[/tex]
The radius - [tex]3[/tex]
