Is it possible to draw a line upto a curve. Something like extend...
I do not know to get the pont on the curve to stop the line.
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
%
\begin{tikzpicture}
%grid
\draw [step=1.0,thin,gray!40]
(0,0) grid (6,5);
\coordinate (C) at (1.5,1.5);
\coordinate (D) at (1.2,3);
\fill[blue] (C) circle (2pt);
\fill[blue] (D) circle (2pt);
\draw (C)--(D);
\draw [red,thick](C)--++(3,0);
\draw [blue,thick](D)--++(3,0);
%
\coordinate (A2) at (5,1);
\coordinate (B2) at (3.0,4);
%
\draw (A2) to [bend left=20] (B2);
%
\end{tikzpicture}
%
\end{document}

Red and blue lines must stop exactly on the curve.
