# Multiple Tangents in Tikz

I would like to draw an ellipse with a large number of tangents drawn on it. Currently my code is very tedious to draw a lot of tangents for and the compiling time takes considerably longer for more and more tangents. Here is my current code:

\documentclass[english]{article}
\usepackage[T1]{fontenc}
\usepackage[latin9]{luainputenc}
\makeatletter
\usepackage{tikz}
\usetikzlibrary{decorations.markings}

\makeatother

\usepackage{babel}
\begin{document}
\begin{tikzpicture}[
tangent/.style={
decoration={
markings,% switch on markings
mark=
at position #1
with
{
\coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
\coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
\coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
}
},
postaction=decorate
},
use tangent/.style={
shift=(tangent point-#1),
x=(tangent unit vector-#1),
y=(tangent orthogonal unit vector-#1)
},
use tangent/.default=1
]
\foreach \x in {0,0.05,...,1.1}
\draw [
tangent=0,
tangent=0.1,
tangent=0.2,
tangent=0.2,
tangent=0.3,
tangent=0.4,
tangent=0.5,
tangent=0.6,
tangent=0.7,
tangent=0.8,
tangent=0.9,
tangent=1.0,
tangent=1.1,
] (-0.25,0)
to [out=-90,in=-90] (1.25,0)
to [out=90,in=90] (-0.25,0);
\begin{scope}
\clip (0,0) circle (1.5);
\draw [thick, use tangent] (-3,0) -- (3,0);
\draw [thick, use tangent=2] (-3,0) -- (3,0);
\draw [thick, use tangent=3] (-3,0) -- (3,0);
\draw [thick, use tangent=4] (-3,0) -- (3,0);
\draw [thick, use tangent=5] (-3,0) -- (3,0);
\draw [thick, use tangent=6] (-3,0) -- (3,0);
\draw [thick, use tangent=7] (-3,0) -- (3,0);
\draw [thick, use tangent=8] (-3,0) -- (3,0);
\draw [thick, use tangent=9] (-3,0) -- (3,0);
\draw [thick, use tangent=10] (-3,0) -- (3,0);
\draw [thick, use tangent=11] (-3,0) -- (3,0);
\end{scope}
\draw (0,0) circle (1.5);
\fill (0,0) circle (0.1) (1,0) circle (0.1);
\end{tikzpicture}
\end{document}


The code produces the following image, which is not that many tangents. So I would like an easy way to draw more tangents around the ellipse inside the circle

With a bit of code reorganisation ;)

\documentclass[english]{article}
\usepackage[T1]{fontenc}
\usepackage[latin9]{luainputenc}
\makeatletter
\usepackage{tikz}
\usetikzlibrary{decorations.markings}

\makeatother

\usepackage{babel}
\begin{document}
\begin{tikzpicture}[
tangent/.style={
decoration={
markings,% switch on markings
mark=
at position #1
with
{
\coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
\coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
\coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
}
},
postaction=decorate
},
use tangent/.style={
shift=(tangent point-#1),
x=(tangent unit vector-#1),
y=(tangent orthogonal unit vector-#1)
},
use tangent/.default=1
]
\begin{scope}
\clip (0,0) circle (1.5);
\foreach \x in {0,0.02,...,1.1}{
\draw [tangent=\x] (-0.25,0) to [out=-90,in=-90] (1.25,0) to [out=90,in=90] (-0.25,0);
\draw [thick, use tangent] (-3,0) -- (3,0);
}
\end{scope}
\draw (0,0) circle (1.5);
\fill (0,0) circle (0.1) (1,0) circle (0.1);
\end{tikzpicture}
\end{document}