Circle of Points with TikZ
Here is my proposition (with comments):
\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\coordinate (c) at (12,3); % center of circle
\def\radius{6cm} % radius of circle
\def\nbpts{400} % nb of points
\def\radpt{.5pt} % radius of points
\colorlet{point color}{red} % color of points
\foreach \numpt in {1,...,\nbpts}{
\fill[point color] (c) ++ (360/\nbpts*\numpt:\radius) circle(\radpt);
}
\end{tikzpicture}
\end{document}
Something like this --replace black color with red
\documentclass[tikz,border=0.5cm]{standalone}
\begin{document}
\begin{tikzpicture}
\foreach \i in {0,5,10,15,20,25,30,...,360}{%
\filldraw [black] (\i:3cm) circle (0.4pt);}
\end{tikzpicture}
\end{document}
EDIT
Circle centre defined at coord (0,0) and given the name {a}
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\node (0,0){a};
\foreach \i in {0,5,10,15,20,25,30,...,360}{%
\filldraw [red] (\i:3cm) circle (0.4pt);}
\end{tikzpicture}
\end{document}
To reduce the number of dots in the circle simply reduce the number of the angles to 45--90--360 as below
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\node (0,0){a};
\foreach \i in {0,45,90,...,360}{%
\filldraw [blue] (\i:3cm) circle (1pt);}
\end{tikzpicture}
\end{document}