%
% ellipse.tex -- Geometrie einer Ellipse
%
% (c) 2022 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{1}
\definecolor{darkgreen}{rgb}{0,0.6,0}
\begin{tikzpicture}[>=latex,thick,scale=\skala]

\def\e{3}

\begin{scope}
\clip (-6.3,-5.5) rectangle (6.3,5.5);
\foreach \s in {7,8,9,11,12,13,14,15,16}{
	%\def\s{9}
	\pgfmathparse{\s/2}
	\xdef\a{\pgfmathresult}
	\pgfmathparse{sqrt(\a*\a-\e*\e)}
	\xdef\b{\pgfmathresult}
	\draw[color=red!30,line width=1.4pt] 
		plot[domain=0:360,samples=100]
			({\a*cos(\x)},{\b*sin(\x)});
}
\end{scope}

\coordinate (O) at (0,0);
\coordinate (F1) at (3,0);
\coordinate (F2) at (-3,0);
\coordinate (A) at (5,0);
\coordinate (Aminus) at (-5,0);
\coordinate (B) at (0,4);

\def\winkel{140}
\pgfmathparse{5*cos(\winkel)}
\xdef\Px{\pgfmathresult}
\pgfmathparse{4*sin(\winkel)}
\xdef\Py{\pgfmathresult}
\coordinate (P) at (\Px,\Py);

\draw[->] (-6.3,0) -- (6.5,0) coordinate[label={$x$}];
\draw[->] (0,-5.6) -- (0,5.8) coordinate[label={right:$y$}];

\draw[color=blue,line width=1pt] (0,0) -- (0,4);
\draw[color=blue,line width=1pt] (0,0) -- (3,0);
\draw[color=blue,line width=1pt] (0,4) -- (3,0);

\draw[color=red,line width=1.4pt] 
	plot[domain=0:360,samples=100]
		({5*cos(\x)},{4*sin(\x)});

\node[color=blue] at ($0.5*(O)+0.5*(F1)$) [above] {$e$};
\node[color=blue] at ($0.5*(O)+0.5*(B)$) [left] {$b$};
\node[color=blue] at ($0.5*(F1)+0.5*(B)$) [above right] {$a$};

\fill[color=darkgreen] (P) circle[radius=0.08];
\node[color=darkgreen] at (P) [above left] {$P$};
\draw[color=darkgreen,line width=1.4pt] (F1) -- (P) -- (F2);
\node[color=darkgreen] at ($0.55*(P)+0.45*(F1)$) [below] {$\overline{F_1P}$};
\node[color=darkgreen] at ($0.50*(P)+0.50*(F2)$) [left] {$\overline{F_2P}$};

\fill[color=red] (A) circle[radius=0.08];
\node[color=red] at (A) [above right] {$A_+$};
\fill[color=red] (Aminus) circle[radius=0.08];
\node[color=red] at (Aminus) [above left] {$A_-$};

\fill[color=blue] (F1) circle[radius=0.08];
\fill[color=blue] (F2) circle[radius=0.08];
\node at (F1) [below right] {$F_1$};
\node at (F2) [below left] {$F_2$};

\end{tikzpicture}
\end{document}