% !TEX TS-program = lualatex
% Created by Alain Matthes on 2025-02-24.

\documentclass{standalone} 
\usepackage{tkz-euclide}
\usepackage{tkz-elements}

\begin{document} 
    
\directlua{
  z.A       = point : new (0, 0)
  z.B       = point : new (1.5 , -3)
  z.C       = point : new (4,1)
  T.ABC     = triangle : new (z.A,z.B,z.C)
  C.ABC     = T.ABC : circum_circle ()
  z.w,z.t   = get_points (C.ABC)
  z.P       = C.ABC : point(-0.15)
  L.steiner = T.ABC : steiner_line (z.P)
  z.sa,z.sb = get_points(L.steiner)
  z.H       = T.ABC.orthocenter
  local PA  = conic : new (z.P,L.steiner,1)
  curve     = PA : points (-5,5,50)
  z.M       = intersection (PA,T.ABC.ca)
}
    
\begin{tikzpicture}
  \tkzGetNodes
  \tkzDrawCoordinates[smooth,red](curve)
  \tkzDrawLines[add = 1 and 1,blue](A,B B,C A,C)
  \tkzDrawLines[cyan,add = .4 and .6](sa,sb)
  \tkzDrawCircle[orange](w,t)
  \tkzDrawPoints (A,B,C,P,H,M)
  \tkzLabelPoints(A,B,C,P,H,M)
\end{tikzpicture}
\end{document}