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%
% kegelschnitt.tex
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{times}
\usepackage{amsmath}
\usepackage{txfonts}
\usepackage[utf8]{inputenc}
\usepackage{graphics}
\usetikzlibrary{arrows,intersections,math,calc}
\usepackage{ifthen}
\begin{document}
\definecolor{kegelfarbe}{rgb}{0.2,0.6,0.6}
\definecolor{ebenenfarbe}{rgb}{0.6,0.4,0.2}
\definecolor{fokusfarbe}{rgb}{0.8,0.0,0.0}
\definecolor{scheitelfarbe}{rgb}{0,0.6,0}
\definecolor{leitfarbe}{rgb}{0.8,0.2,0.8}
\newboolean{showgrid}
\setboolean{showgrid}{false}
\def\breite{7}
\def\hoehe{5}
\begin{tikzpicture}[>=latex,thick]
% Povray Bild
\node at (0,0) {\includegraphics[width=14cm]{kegelschnitte.jpg}};
% Gitter
\ifthenelse{\boolean{showgrid}}{
\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
\draw (-\breite,-\hoehe) grid (\breite, \hoehe);
\fill (0,0) circle[radius=0.05];
}{}
\begin{scope}[yshift=-7.5cm]
\begin{scope}
\clip (-2,-2.5) rectangle (2,1.5);
\fill[color=kegelfarbe!40]
(-1.4,-3) -- (1.4,-3) -- (-1.4,3) -- (1.4,3) -- cycle;
\begin{scope}[xshift=0.5cm]
\draw[color=ebenenfarbe,line width=1.4pt]
(-1.4,-3) -- (1.4,3);
\end{scope}
\end{scope}
\begin{scope}[xshift=-4.5cm]
\clip (-2,-2.5) rectangle (2,1.5);
\fill[color=kegelfarbe!40]
(-1.4,-3) -- (1.4,-3) -- (-1.4,3) -- (1.4,3) -- cycle;
\begin{scope}[xshift=-0.3cm]
\draw[color=ebenenfarbe,line width=1.4pt] (-0.4,-3) -- (0.4,3);
\end{scope}
\end{scope}
\begin{scope}[xshift=4.5cm]
\clip (-2,-2.5) rectangle (2,1.5);
\fill[color=kegelfarbe!40]
(-1.4,-3) -- (1.4,-3) -- (-1.4,3) -- (1.4,3) -- cycle;
\begin{scope}[xshift=0.9cm]
\draw[color=ebenenfarbe,line width=1.4pt] (-3.4,-3) -- (3.4,3);
\end{scope}
\end{scope}
\end{scope}
\def\marke#1#2#3#4{
\fill[color=white,opacity=0.5]
({#1-0.25},{#2-0.2}) rectangle ({#1+0.20},{#2+0.2});
\node[color=#3] at ({#1},{#2}) {#4};
}
\node[color=fokusfarbe] at (-5,0.5) {$F_1$};
\node[color=fokusfarbe] at (-4.5,4.4) {$F_2$};
%\node[color=scheitelfarbe] at (-4.5,4.1) [below left] {$S_2$};
%\node[color=scheitelfarbe] at (-4.7,0.8) [above left] {$S_1$};
\marke{-4.9}{3.7}{scheitelfarbe}{$S_2$}
\marke{-5.1}{1.1}{scheitelfarbe}{$S_1$}
\node[color=yellow] at (-3.9,-0.9) [right] {$P$};
\node[color=fokusfarbe] at (0.05,0.75) {$F$};
%\node[color=scheitelfarbe] at (0.4,1.0) [above left] {$S$};
\marke{0.35}{1.4}{scheitelfarbe}{$S$};
\node[color=yellow] at (0.95,-0.6) [right] {$P$};
\node[color=leitfarbe] at (2.2,1.2) {$l$};
\node[color=fokusfarbe] at (3.5,-2.9) {$F_1$};
\node[color=fokusfarbe] at (4.4,-0.8) {$F_2$};
%\node[color=scheitelfarbe] at (3.6,-3.5) [below left] {$S_1$};
%\node[color=scheitelfarbe] at (4.8,-0.4) [above right] {$S_2$};
\marke{3.05}{-3.85}{scheitelfarbe}{$S_1$}
\marke{5.3}{-0.0}{scheitelfarbe}{$S_2$}
\node[color=yellow] at (4.8,-2.7) [below right] {$P$};
\begin{scope}[yshift=-5.5cm]
\node at (-4.5,0)
{Hyperbel: $\overline{F_1P}-\overline{F_2P}=\text{const}$\strut};
\fill[color=white,opacity=0.7] (-1.3,-0.25) rectangle (1.3,0.25);
\node at (0,0) {Parabel: $\overline{FP}=\overline{lP}$\strut};
\fill[color=white,opacity=0.7] (2.4,-0.25) rectangle (6.6,0.25);
\node at (4.5,0)
{Ellipse: $\overline{F_1P}+\overline{F_2P}=\text{const}$\strut};
\end{scope}
\end{tikzpicture}
\end{document}
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