Blocking Sets of Certain Line Sets Related to a Conic

In this paper we classify point sets of minimum size of two types (1) point sets meeting all secants to an irreducible conic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal C}$$\end{document} of the desarguesian projective plane PG(2,q), q odd; (2) point sets meeting all external lines and tangents to a given irreducible conic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal C}$$\end{document} of the desarguesian projective plane PG(2,q), q even.