# Tangent on parabola

I really was working on this now for a long time. I need a tangent line on a parabola; here is my working example:

\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{arrows,calc,intersections,decorations.markings}
\usepackage{relsize}
\begin{document}
\begin{tikzpicture}[
]
\draw[very thick, ->, >=stealth', line join=miter]   (6,0) node(xline)[right] {$x_i$} -|
(0,6) node(yline)[above] {$y_i$};
\draw[blue,thick,name path = line 1]          (4,1) coordinate () parabola (0,3);
\draw[blue,thick,name path = line 2]         (4,2) coordinate ( ) parabola (0,4);
\draw[blue,thick,name path = line 3]         (4,3) coordinate ( ) parabola (0,5);
\draw[dashed ,name path = line 4](1,0) coordinate () -- (1,5);
\draw[dashed ,name path = line 5](3,0) coordinate () -- (3,5);
\fill[red,name intersections={of=line 1 and line 4}]     (intersection-1) circle (2pt) node { };
\end{tikzpicture}
\end{document}


Instead of the red dot I want a tangent line. Does anyone of you know how to do this?

\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);
}
},
postaction=decorate
},
use tangent/.style={
shift=(tangent point-#1),
x=(tangent unit vector-#1),
},
use tangent/.default=1
]
\draw[thick, <->, line join = miter->]   (6,0) node(xline)[right] {$x_i$} -|
(0,6) node(yline)[above] {$y_i$};
\draw[dashed ,name path = line1](1,0) coordinate () -- (1,5);
\draw [blue,tangent=0.3,name path = line2] (4,1)    parabola  (0,3);
\fill[red,name intersections={of=line1 and line2}]     (intersection-1) circle (2pt) node {};
\draw [orange, thick, use tangent] (-1,0) -- (1,0) ;
\end{tikzpicture}

-
have you seen these questions – cmhughes Sep 28 '12 at 16:38
Welcome to TeX.SE. Let us know if any of those questions provided you with a solution you could use. – Peter Grill Sep 28 '12 at 18:43
Hi! Thanks Herbert for adding the pic! - and cmhughes I saw these examples and I wanted to use the intersection thing. I guess this tex.stackexchange.com/questions/25928/… best describes what I want but I was not able to modify the code as I want; how do you define the tangent to be on the intersection? Is there any way to say tangent = intersection? – Gine Oct 1 '12 at 9:32
I have added the new piece of code above! (...how can I add a comment of more than 600 characters? :-) sorry...) – Gine Oct 1 '12 at 9:39
Have a Look at tex.stackexchange.com/questions/60392/… – Uwe Ziegenhagen Oct 2 '12 at 1:25

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{arrows, intersections}

\begin{document}

\begin{tikzpicture}
[
extended line/.style={shorten >=-#1,shorten <=-3cm}
, extended line/.default=1cm
]

\clip (-2, -1) rectangle (7,8);

\draw [very thick, <->, >=stealth', line join=miter]
(6,0) node (xline)[right] {$x_i$} -|
(0,7) node (yline) [above] {$y_i$}
;

\draw [blue, ultra thick, name path = my parabola] (5,1) parabola (1,7);
\draw [name path = my reference] (2,0) -- (2,5);

\draw [dotted, name path = line 1] (4   , 0) -- (4   , 5);
\draw [dotted, name path = line 2] (3   , 0) -- (3   , 5);
\draw [dotted, name path = line 3] (2.01, 0) -- (2.01, 5);

\fill [name intersections = {of = my parabola and my reference, name = my dot}];

\fill [name intersections = {of = my parabola and line 1, name = i1}];
\fill [name intersections = {of = my parabola and line 2, name = i2}];
\fill [name intersections = {of = my parabola and line 3, name = i3}];

\fill [red]    (i1-1) circle (1.1pt);
\fill [orange] (i2-1) circle (1.1pt);
\fill [black]  (i3-1) circle (1.1pt);

\draw [red   , extended line             ] (my dot-1) -- (i1-1);
\draw [orange, extended line = 2cm       ] (my dot-1) -- (i2-1);
\draw [black , extended line = 4cm, thick] (my dot-1) -- (i3-1);

\end{tikzpicture}
\end{document}

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