Why I am only getting one point of intersection read by the program? Solution is to breaking to two parts with tangent lines drawn at different lengths.

```
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,intersections}
\usetikzlibrary{decorations.markings}
\begin{document}
\pgfkeys{tikz/.cd,
 tangent length/.store in=\TangentLength,
 tangent length=3.14cm,
 normal length/.store in=\NormalLength,
 normal length=7mm}
 \newcounter{tangent}
 \newcounter{normal}
 \tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
 tangent at/.style={postaction={decorate,decoration={markings,
 mark=at position #1 with {\stepcounter{tangent}
 \draw[tangent,name path=tangent-\thetangent] (-\TangentLength,0) -- 
 (9cm,0);
 \fill[tangent] (0,0) circle (2pt);}}}},
  normal at/.style={postaction={decorate,decoration={markings,
   mark=at position #1 with {\stepcounter{normal}
 \draw[normal,name path=normal-\thenormal] (0,-\NormalLength) -- 
 (0,\NormalLength);
 \fill[normal] (0,0) circle (2pt);}}}}, 
 }
 \begin{tikzpicture}
 % Axes
 \draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
 \draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
 % Origin
 \node at (0,0) [below left] {$0$};
 % Points
 \coordinate (start) at (1,-0.8);
 \coordinate (c1) at (3,3);
 \coordinate (c2) at (5.5,1.5);
 \coordinate (c3) at (8,4);
 \coordinate (end) at (10.5,-0.8);
 % show the points
 % \foreach \n in {start,c1,c2,c3,end} \fill [black] (\n)
 %     circle (2pt) node [below] {}; 
 %  join the coordinates
\draw [name path=curve,thick,tangent at/.list={0.3,0.3},
  normal at/.list={}] (start) to[out=70,in=180] (c1) to[out=0,in=180]
  (c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
 \fill[name intersections={of=curve and tangent-2,total=\t},cyan]
 (intersection-\t) circle (2pt);
  \fill[name intersections={of=curve and tangent-1,total=\t},cyan]
  (intersection-\t) circle (2pt);
 \end{tikzpcicture}
 \end{document}

```

This outputs:

[![enter image description here](https://i.stack.imgur.com/r7mmR.png)](https://i.stack.imgur.com/r7mmR.png)