Answer
Center is $(2,-4)$ and radius is $\sqrt{17}$.
Work Step by Step
Manipulate to the equation to get the form $(x-h)^2+(y-k)^2=r^2$ where $(h,k)$ is center and $r$ is radius of a circle:
$$x^2+y^2-4x+8y+3=0$$
Reorder the terms:
$$x^2-4x+y^2+8y+3=0$$
Add and subtract the same values to complete each square:
$$x^2-4x+4-4+y^2+8y+16-16+3=0$$
Write each as a complete square:
$$(x-2)^2-4+(y+4)^2-16+3=0$$
Add the constants and move to the right:
$$(x-2)^2+(y+4)^2=17$$
Rewrite as:
$$(x-2)^2+(y-(-4))^2=\sqrt{17}^2$$
Hence, center is $(2,-4)$ and radius is $\sqrt{17}$.
