# Reflecting object in tikzpicture

I'm trying to use tikzpicture to draw the different conics.

To finish, I want to reflect the two arcs I drew around the y axis to get a hyperbola but I don't know how to do that. The reflected part does not appear where I want it to.

This is my code:

\begin{tikzpicture}

\draw (0,0) ellipse (1cm and 0.3cm);

\draw (0,-3) -- (-1,0);

\draw (0,-3) -- (1,0);

\draw (-1,-6) -- (0,-3);

\draw (1,-6) -- (0,-3);

\draw (0,-6) ellipse (1cm and 0.3 cm);

\draw (2,-3) circle (0.75cm);

\draw (4.5,-3) ellipse (1cm and 0.4 cm);

\draw (7,-3.5) parabola (6.5,-2) ;

\draw (7,-3.5) parabola (7.5,-2);

\draw (9, -2.5) arc (5:45:2);

\draw (9, -2.5) arc (5:-45:2);

\end{tikzpicture}


I get this:

To reflect the arcs I use this code:

\begin{scope}[yscale=1,xscale=-1]
\draw (9, -2.7) arc (5:45:1);
\draw (9, -2.7) arc (5:-45:1);
\end{scope}


But then I get this:

Can someone help me fix this ? Any help is appreciated. Thank you all in advance !

The reason why the arc moves so far is that the horizontal coordinate 9 gets mapped to -9. One convenient way of reflecting things is to draw them in a pic, which can be reflected (or transformed otherwise). I do not know the relation between the two arcs, but you may adjust the horizontal coordinate, which is now -0.5, to get what you want. (Or you give me a hint.)

\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\begin{tikzpicture}[pics/my arc/.style={code={
\draw (-0.5, -2.5) arc (5:45:2);
\draw (-0.5, -2.5) arc (5:-45:2);}}]

\draw (0,0) ellipse (1cm and 0.3cm);

\draw (0,-3) -- (-1,0);

\draw (0,-3) -- (1,0);

\draw (-1,-6) -- (0,-3);

\draw (1,-6) -- (0,-3);

\draw (0,-6) ellipse (1cm and 0.3 cm);

\draw (2,-3) circle (0.75cm);

\draw (4.5,-3) ellipse (1cm and 0.4 cm);

\draw (7,-3.5) parabola (6.5,-2) ;

\draw (7,-3.5) parabola (7.5,-2);

\path (9,0) pic {my arc} pic[xscale=-1] {my arc};

\end{tikzpicture}
\end{document}


Alternatively you could introduce a style that reflects at shifted x or y axes.

\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\begin{tikzpicture}[reflect at x/.style={xshift=#1*1cm,xscale=-1,xshift=-1*#1*1cm},
reflect at y/.style={yshift=#1*1cm,yscale=-1,yshift=-1*#1*1cm}]
\draw (0,0) ellipse (1cm and 0.3cm);
\draw (0,-3) -- (-1,0);
\draw (0,-3) -- (1,0);
\draw (-1,-6) -- (0,-3);
\draw (1,-6) -- (0,-3);
\draw (0,-6) ellipse (1cm and 0.3 cm);
\draw (2,-3) circle (0.75cm);
\draw (4.5,-3) ellipse (1cm and 0.4 cm);
\draw (7,-3.5) parabola (6.5,-2) ;
\draw (7,-3.5) parabola (7.5,-2);
\draw (9, -2.5) arc (5:45:2);
\draw (9, -2.5) arc (5:-45:2);
\begin{scope}[reflect at x=9.5]
\draw (9, -2.5) arc (5:45:2);
\draw (9, -2.5) arc (5:-45:2);
\end{scope}
\end{tikzpicture}
\end{document}