I'd like to draw a set of curves, each tangent to a different point on a given line. The requirement is that the curves are convex and downward sloping.
In the following MWE, I use the to[out=<x>,in=<y>]
operation to manually adjust the slope of the curves so that they appear to be tangent at the desired point. This requires a lot of trial-and-errors and the result is not ideal. Is there a better way to draw such curves?
MWE
\documentclass[border=2pt,tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\foreach \i in {1,2,3,4}{
\draw[thick](0,4.5)--(7,0)coordinate[pos=\i/5](\i);
\fill(\i)circle[radius=2pt]node[below left]{pt \i};
\draw[red](\i)to[out=140,in=-80]++(-1,1.5) (\i)to[out=-25,in=170]++(1.25,-.4);
}
\draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};
\end{tikzpicture}
\end{document}