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Diffstat (limited to 'buch/chapters/030-geometrie/images/hyperbel.tex')
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diff --git a/buch/chapters/030-geometrie/images/hyperbel.tex b/buch/chapters/030-geometrie/images/hyperbel.tex new file mode 100644 index 0000000..adee7da --- /dev/null +++ b/buch/chapters/030-geometrie/images/hyperbel.tex @@ -0,0 +1,89 @@ +% +% 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} + |