How to add patterns inside shapes bounded by curves?

Question

It is easy to use patterns for nice shapes like rectangle. How to fill an area by patterns enclosed by some curves? For example I have trouble with adding pattern to the following between two arcs:

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
\draw  (-1,1) node (v1) {} circle (4.5);
\draw  (v1) circle (2.5);
\draw (-5.5,1) arc (180:360:1 and .25);
\draw (1.5,1) arc (180:360:1 and .25);
\end{tikzpicture}
\end{document}

Answer 1

You need a closed shape to use patterns or fill. Shapes bounded by curves can be converted or redrawn like this:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture}
\draw[pattern=horizontal lines] (-5.5,1) arc (180:360:1 and .25) arc (180:360:2.5) arc (180:360:1 and .25) arc (0:-180:4.5) -- cycle;
\end{tikzpicture}
\end{document}

Answer 2

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\draw  (-1,1) node (v1) {} circle (4.5);
\draw  (v1) circle (2.5);

\fill[red](-5.5,1) arc (180:360:1 and .25)
arc(180:0:2.5)
arc (180:360:1 and .25)
arc (0:180:4.5) ;
\end{tikzpicture}
\end{document}