Parabola

The intersection point of y = 0 with first line is B(–p, 0).
The intersection point of y = 0 with second line is A(–q, 0).
The intersection point of the two lines is C(pq, (p + 1)(q + 1)).
The altitude from C to AB is x = pq.
The altitude from B to AC is
y = -

q

1+q

(x+p)
Solving these two equations, we get x = pq and y = – pq.
Hence, the locus of orthocentre is x + y = 0.