\VDDdef L(-4,-1)R(4,4)F(1,1.5)F'(2,-1)
\VDDdeflinepoint l:O(0,0)O'(4,1) % l = directrix
\VDDcleadline p:l:F
\VDDcintersect V:pl
\VDDcabstransp Q:V:O'O:2         % Q = point on directrix
\VDDdeflinepoint m:QF            % m = line through Q and F 
\VDDcavg M:QF
\VDDcleadline n:m:M              % n perpendicular bisector of QF
\VDDcleadline k:l:Q              % k perpendicular to directrix in Q
\VDDcintersect P:kn              % P point on parabola
\VDDdcanvas1:1
  \VDDdef O''(8,2)
  \VDDdpoint FF'
  \VDDdperp OQP
  \VDDdperp FMP
  \VDDdwholeline lkn
  \VDDdlinepartequal FMMQ
  \VDDdlinepartequal FPPQ
  \VDDdline PFQ
  \VDDlpointany OO'O'':$l$
  \VDDlpointletter QFP
  \VDDdparabola F:l              % draw parabola determined by F and l
  \VDDdparabola F':l              % draw parabola determined by F' and l
\VDDdcanvasend
