Fundamental groups of some quadric-line arrangements
  In this paper we obtain presentations of fundamental groups of the complements of three quadric-line arrangements in P^2. The first arrangement is a smooth quadric Q with n tangent lines to Q, and the second one is a quadric Q with n lines passing through a point p not in Q. The last arrangement consists of a quadric Q with n lines passing through a point p in Q. 
Meirav Amram, Mina Teicher, Muhammed Uludag