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%
% ellipse.tex -- Abbildung der Ellipsen zur Herleitung der Jacobi
% elliptischen Funktionen
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math,calc}
\begin{document}
\def\skala{0.72}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\definecolor{darkgreen}{rgb}{0,0.6,0}
% add image content here
\def\winkel{70}
\def\a{5}
\def\b{3}
\pgfmathparse{sqrt(\a*\a-\b*\b)}
\xdef\e{\pgfmathresult}
\fill[color=gray!20] (0,0) -- plot[domain=0:\winkel,samples=100]
({5*cos(\x)},{3*sin(\x)})
-- cycle;
\draw (0,0) -- ({5*cos(\winkel)},{3*sin(\winkel)});
\draw[color=red,line width=1.4pt] plot[domain=0:\winkel,samples=100]
({5*cos(\x)},{3*sin(\x)});
\node at (5,0) [below right] {$a$};
\node at (0,3) [above left] {$b$};
\fill[color=red] ({5*cos(\winkel)},{3*sin(\winkel)}) circle[radius=0.08];
\draw[color=red,line width=1pt] (0,0) ellipse (5cm and 3cm);
%\node at ({5*cos(\winkel/2)},{3*sin(\winkel/2)}) [above right] {$u$};
\node at ({5*cos(\winkel)},{3*sin(\winkel)}) [above right] {$P=(x,y)$};
\draw[->] (-5.2,0) -- (5.8,0);% coordinate[label={$x$}];
\draw[->] (0,-3.2) -- (0,3.8);% coordinate[label={right:$y$}];
\draw[color=darkgreen] (0,0) -- (\e,0);
\draw[color=darkgreen] (0,0) -- (-\e,0);
\node[color=darkgreen] at ({0.5*\e},0) [below] {$e$};
\node[color=darkgreen] at ({-0.5*\e},0) [below] {$-e$};
\fill[color=blue] ({-\e},0) circle[radius=0.08];
\node[color=blue] at (-\e,0) [below] {$F_1$};
\fill[color=blue] ({\e},0) circle[radius=0.08];
\node[color=blue] at (\e,0) [below] {$F_2$};
\draw[color=blue] (0,3) -- (\e,0);
\draw[color=blue] (0,3) -- (-\e,0);
\node[color=blue] at ($0.5*(0,3)+0.5*(\e,0)$) [below left] {$a$};
\node[color=blue] at ($0.5*(0,3)+0.5*(-\e,0)$) [below right] {$a$};
\fill[color=red] (0,3) circle[radius=0.08];
\node at (0,0) [below left] {$O$};
\begin{scope}[xshift=-9.5cm]
\fill[color=gray!20] (0,0) -- (3,0) arc (0:70:3) -- cycle;
\node[color=red] at (35:3) [above right] {$\varphi$};
\draw (0,0) -- (70:3);
\node at (70:1.7) [left] {$r$};
\draw[->] (-3.2,0) -- (3.8,0);% coordinate[label={$x$}];
\draw[->] (0,-3.2) -- (0,3.8);% coordinate[label={right:$y$}];
\draw[color=red,line width=1pt] (0,0) circle[radius=3];
\draw[color=red,line width=1.4pt] (3,0) arc (0:70:3);
\fill[color=red] (70:3) circle[radius=0.08];
\node at (70:3) [above right] {$P=(x,y)$};
\node at (0,0) [below left] {$O$};
\end{scope}
\end{tikzpicture}
\end{document}
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