%
% hyperbel.tex -- Hyperbel-Definition
%
% (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}
\pgfmathparse{14/18.8}
\xdef\skala{\pgfmathresult}
\def\hyperbel#1#2#3{
\begin{scope}
	\clip (-9,-7) rectangle (9,7);
	\draw[color=#3,line width=1.4pt] plot[domain=-2:2,samples=100]
		({#1*cosh(\x)},{#2*sinh(\x)});
	\draw[color=#3,line width=1.4pt] plot[domain=-2:2,samples=100]
		({-#1*cosh(\x)},{#2*sinh(\x)});
\end{scope}
}
\definecolor{darkgreen}{rgb}{0,0.6,0}
\def\punkt#1#2#3{ ({#1*cosh(#3)},{#2*sinh(#3)}) }
\begin{tikzpicture}[>=latex,thick,scale=\skala]

\def\e{5}

\coordinate (F1) at (\e,0);
\coordinate (F2) at (-\e,0);

\draw[->] (-9.1,0) -- (9.4,0) coordinate[label={$x$}];
\draw[->] (0,-7.1) -- (0,7.3) coordinate[label={right:$y$}];


\begin{scope}
\clip (-9,-7) rectangle (9,7);

\draw[color=gray] (-12,-9) -- (12,9);
\draw[color=gray] (-12,9) -- (12,-9);
\end{scope}

\foreach \a in {0.5,1,...,4.5}{
	\pgfmathparse{sqrt(\e*\e-\a*\a)}
	\xdef\b{\pgfmathresult}
	\hyperbel{\a}{\b}{red!20}
}

\def\a{4}
\def\b{3}
\def\t{1.2}
%\coordinate (P) at \punkt{\a}{\b}{\t};
\coordinate (P) at ({1.8107*\a},{1.5095*\b});

\draw[color=gray] (\e,0) arc (0:atan(\b/\a):\e);

\draw[color=darkgreen,line width=1.4pt] (F1) -- (P) -- (F2);

\draw[color=blue,line width=1.4pt] (0,0) -- (\a,0) -- (\a,\b);
\node[color=blue] at ({0.5*\a},0) [above] {$a$};
\node[color=blue] at (\a,{0.5*\b}) [left] {$b$};

\fill[color=blue] (F1) circle[radius=0.10];
\fill[color=blue] (F2) circle[radius=0.10];

\hyperbel{\a}{\b}{red}

\node at (F1) [above left] {$F_1$};
\node at (F2) [above left] {$F_2$};

\node[color=blue] at (F1) [below] {$e$};
\node[color=blue] at (F2) [below] {$-e$};

\fill[color=darkgreen] (P) circle[radius=0.1];
\node[color=darkgreen] at (P) [below right]  {$P$};

\fill[color=red] (\a,0) circle[radius=0.1];
\node[color=red] at (\a,0) [below left] {$A_+$};
\fill[color=red] (-\a,0) circle[radius=0.1];
\node[color=red] at (-\a,0) [below right] {$A_-$};

\node[color=darkgreen] at ($0.5*(F2)+0.5*(P)$) [above left] {$\overline{F_2P}$};
\node[color=darkgreen] at ($0.5*(F1)+0.5*(P)$) [right] {$\overline{F_1P}$};

\end{tikzpicture}
\end{document}