yes d
derive orthocentre as (pq , -pq)
coming to a very crude way of obtaining solution, substitute n=2
The locus of the orthocenter of the triangle formed by the lines
(1+p)x-py+p(1+p)=0
(1+q)x-qy+q(1+q)=0
and y=0 where p≠q is
hyperbola
parabola
ellipse
straight line